×
Krylov, P. A.; Tuganbaev, A. A.

Modules over discrete valuation domains. III. (English. Russian original) Zbl 1472.13018

J. Math. Sci., New York 258, No. 2, 199-221 (2021); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 164, 74-95 (2019).
Summary: This review paper is a continuation of two previous review papers devoted to properties of modules over discrete valuation domains. The first part of this work was published in [the authors, J. Math. Sci., New York 145, No. 4, 4997–5117 (2007; Zbl 1178.13012); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 121 (2006); J. Math. Sci., New York 151, No. 5, 3255–3371 (2008; Zbl 1229.13018); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 122 (2006)]. In this review paper, we preserve the numeration of chapters and sections of parts I and II. The first part consists of Chapter 9 “Appendix,” Secs. 40-42. In Sec. 40, we consider \(p\)-adic torsion-free modules with isomorphic automorphism groups. Section 41 is devoted to torsion-free modules over a complete discrete valuation domain with isomorphic radicals of their endomorphism rings. The volume of the paper does not allow us to provide the proofs of all the results that appeared after publication of the previous parts and directly related to the issues under consideration in it. In the final Sec. 42, we describe some of these new results.

MSC:

13C05 Structure, classification theorems for modules and ideals in commutative rings
13F30 Valuation rings
13F10 Principal ideal rings

Keywords:

discrete valuation domain; \(p\)-adic module; endomorphism ring

Citations:

Zbl 1178.13012; Zbl 1229.13018
Cite Review PDF
Full Text: DOI

References:

[1] Ali, MM, Invertibility of multiplication modules, New Zealand J. Math., 35, 17-29 (2006) · Zbl 1099.13020
[2] Anderson, FW; Fuller, KR, Rings and Categories of Modules (1974), New York: Springer-Verlag, New York · Zbl 0301.16001 · doi:10.1007/978-1-4684-9913-1
[3] Arnautov, VI; Glavatsky, ST; Mikhalev, AV, Introduction to the Theory of Topological Rings and Modules (1995), New York: Marcel Dekker, New York · Zbl 0842.16001
[4] Arnold, D., A duality for torsion-free modules of finite rank over a discrete valuation ring, Proc. London Math. Soc., 24, 204-216 (1972) · Zbl 0237.13016 · doi:10.1112/plms/s3-24.2.204
[5] Arnold, D., A duality for quotient divisible Abelian groups of finite rank, Pac. J. Math., 42, 11-15 (1972) · Zbl 0262.20062 · doi:10.2140/pjm.1972.42.11
[6] Arnold, D., Exterior powers and torsion free modules over discrete valuation rings, Trans. Am. Math. Soc., 170, 471-481 (1972) · Zbl 0295.13003 · doi:10.1090/S0002-9947-1972-0304367-1
[7] Arnold, D., Finite rank torsion-free Abelian groups and rings, Lect. Notes Math., 931, 1-191 (1982) · Zbl 0493.20034 · doi:10.1007/BFb0094246
[8] Arnold, D., A finite global Azumaya theorem in additive categories, Proc. Am. Math. Soc., 91, 1, 25-30 (1984) · Zbl 0538.18007 · doi:10.1090/S0002-9939-1984-0735557-5
[9] Arnold, D., Abelian Groups and Representations of Finite Partially Ordered Sets (2000), New York: Springer-Verlag, New York · Zbl 0959.16011 · doi:10.1007/978-1-4419-8750-1
[10] Arnold, D., Direct sums of local torsion-free Abelian groups, Proc. Am.Math. Soc., 130, 6, 1611-1617 (2001) · Zbl 0998.20046 · doi:10.1090/S0002-9939-01-06246-3
[11] Arnold, D.; Dugas, M., Indecomposable modules over Nagata valuation domains, Proc. Am. Math. Soc., 122, 689-696 (1994) · Zbl 0824.13007 · doi:10.1090/S0002-9939-1994-1239795-3
[12] Arnold, D.; Dugas, M., Representation type of posets and finite rank Butler groups, Colloq. Math., 74, 299-320 (1997) · Zbl 0909.20036 · doi:10.4064/cm-74-2-299-320
[13] Arnold, D.; Dugas, M., Co-purely indecomposable modules over discrete valuation rings, J. Pure Appl. Algebra, 161, 1-12 (2001) · Zbl 0989.13005 · doi:10.1016/S0022-4049(00)00091-8
[14] Arnold, D.; Dugas, M.; Rangaswamy, KM, Finite rank Butler groups and torsion-free modules over a discrete valuation ring, Proc. Am. Math. Soc., 129, 325-335 (2001) · Zbl 0979.20049 · doi:10.1090/S0002-9939-00-05547-7
[15] Arnold, D.; Dugas, M.; Rangaswamy, KM, Torsion-free modules of finite rank over a discrete valuation ring, J. Algebra, 272, 2, 456-469 (2004) · Zbl 1092.13015 · doi:10.1016/j.jalgebra.2003.09.042
[16] Arnold, D.; Hunter, R.; Richman, F., Global Azumaya theorems in additive categories, J. Pure Appl. Algebra, 16, 223-242 (1980) · Zbl 0443.18014 · doi:10.1016/0022-4049(80)90026-2
[17] Arnold, D.; Rangaswamy, KM, Mixed modules of finite torsion-free rank over a discrete valuation domain, Forum Math., 18, 1, 85-98 (2006) · Zbl 1097.13009 · doi:10.1515/FORUM.2006.004
[18] Arnold, D.; Rangaswamy, KM; Richman, F., Pi-balanced torsion-free modules over a discrete valuation domain, J. Algebra, 295, 1, 269-288 (2006) · Zbl 1109.13008 · doi:10.1016/j.jalgebra.2005.02.003
[19] Arnold, D.; Richman, F., Subgroups of finite direct sums of valuated cyclic groups, J. Algebra, 114, 1, 1-15 (1988) · Zbl 0666.20025 · doi:10.1016/0021-8693(88)90207-4
[20] Arnold, J., Power series rings over discrete valuation rings, Pac. J. Math., 93, 1, 31-33 (1981) · Zbl 0438.13016 · doi:10.2140/pjm.1981.93.31
[21] Artin, E., Geometric Algebra (1957), New York: Interscience Publ, New York · Zbl 0077.02101
[22] Astuti, P.; Wimmer, HK, Stacked submodules of torsion modules over discrete valuation domains, Bull. Austr. Math. Soc., 68, 3, 439-447 (2003) · Zbl 1049.13005 · doi:10.1017/S0004972700037849
[23] P. Astuti and H. K. Wimmer, “Regular submodules of torsion modules over discrete valuation domains,” arXiv 1601.06356v1 [math. AC]. · Zbl 1049.13005
[24] Atiyah, M., On the Krull-Schmidt theorem with applications to sheaves, Bull. Soc. Math. Fr., 84, 307-317 (1956) · Zbl 0072.18101 · doi:10.24033/bsmf.1475
[25] Auslander, M.; Reiten, I.; Smalø, SO, Representation Theory of Artin Algebras, Cambridge Univ (1995), Cambridge: Press, Cambridge · Zbl 0834.16001 · doi:10.1017/CBO9780511623608
[26] Azumaya, G., Corrections and supplementaries to my paper concerning Krull-Remak-Schmidt’s theorem, Nagoya Math. J., 1, 117-124 (1950) · Zbl 0040.01201 · doi:10.1017/S002776300002290X
[27] Baer, R., Abelian groups that are direct summands of every containing Abelian group, Bull. Am. Math. Soc., 46, 800-806 (1940) · JFM 66.0074.02 · doi:10.1090/S0002-9904-1940-07306-9
[28] Baer, R., A unified theory of projective spaces and finite Abelian groups, Trans. Am. Math. Soc., 52, 283-343 (1942) · Zbl 0063.00165 · doi:10.1090/S0002-9947-1942-0007252-9
[29] Baer, R., Automorphism rings of primary Abelian operator groups, Ann. Math., 44, 192-227 (1943) · Zbl 0061.05405 · doi:10.2307/1968763
[30] Baer, R., Linear Algebra and Projective Geometry (1952), New York: Academic Press, New York · Zbl 0049.38103
[31] Bass, H., Algebraic K-Theory (1968), New York: Benjamin, New York · Zbl 0174.30302
[32] Beaumont, RA; Pierce, RS, Torsion-free rings, Ill. J. Math., 5, 61-98 (1961) · Zbl 0108.03802
[33] Beaumont, RA; Pierce, RS, Subrings of algebraic number fields, Acta Sci. Math. Szeged., 22, 202-216 (1961) · Zbl 0117.02807
[34] Beaumont, RA; Pierce, RS, Some invariant of p-groups, Michigan Math. J., 11, 138-149 (1964) · Zbl 0126.26903 · doi:10.1307/mmj/1028999085
[35] Beaumont, RA; Pierce, RS, Isomorphic direct summands of abelian groups, Math. Ann., 153, 1, 21-37 (1964) · Zbl 0122.27801 · doi:10.1007/BF01361704
[36] Blagoveshchenskaya, E.; Ivanov, G.; Schultz, P., The Baer-Kaplansky theorem for almost completely decomposable groups, Contemp. Math., 273, 85-93 (2001) · Zbl 0985.20044 · doi:10.1090/conm/273/04425
[37] N. Bourbaki, Algébre Commutative, Hermann, Paris (1961, 1964, 1965).
[38] Bowshell, RA; Schultz, P., Unital rings whose additive endomorphisms commute, Math. Ann., 228, 3, 197-214 (1977) · Zbl 0336.20040 · doi:10.1007/BF01420290
[39] Breaz, S., On a class of mixed groups with semi-local Walk-endomorphism ring, Commun. Algebra, 30, 9, 4473-4485 (2002) · Zbl 1014.20027 · doi:10.1081/AGB-120013333
[40] Carroll, D.; Goldsmith, B., On transitive and fully transitive Abelian p-groups, Proc. Roy. Irish Acad., 96A, 1, 33-41 (1996) · Zbl 0881.20024
[41] Cartan, H.; Eilenberg, S., Homological Algebra, Princeton Univ (1956), Princeton: Press, Princeton · Zbl 0075.24305
[42] Chekhlov, AR, On decomposable fully transitive torsion-free Abelian groups, Sib. Mat. Zh., 42, 3, 714-719 (2001) · Zbl 1003.20048 · doi:10.1023/A:1010491630413
[43] Chekhlov, AR, On one class of endotransitive groups, Mat. Zametki, 69, 6, 944-949 (2001) · Zbl 1016.20037 · doi:10.4213/mzm709
[44] Chekhlov, AR, Fully transitive torsion-free Abelian groups of finite p-rank, Algebra Logika, 40, 6, 698-715 (2001) · Zbl 1017.20046 · doi:10.1023/A:1013755809961
[45] A. R. Chekhlov, Abelian groups with many endomorphisms [in Russian], thesis, Tomsk (2003).
[46] Chekhlov, AR; Krylov, PA, On L. Fuchs’ problems 17 and 43, J. Math. Sci., 143, 5, 3517-3602 (2007) · Zbl 1154.20046 · doi:10.1007/s10958-007-0223-1
[47] Corner, ALS, Every countable reduced torsion-free ring is an endomorphism ring, Proc. London Math. Soc., 13, 3, 687-710 (1963) · Zbl 0116.02403 · doi:10.1112/plms/s3-13.1.687
[48] A. L. S. Corner, “Endomorphism rings of torsion-free Abelian groups,” in: Proc. Int. Conf. Theory of Groups, Canberra (1965), pp. 59-60. · Zbl 0178.02303
[49] Corner, ALS, On endomorphism rings of primary Abelian groups, Quart. J. Math. Oxford, 20, 79, 277-296 (1969) · Zbl 0205.32506 · doi:10.1093/qmath/20.1.277
[50] Corner, ALS, The independence of Kaplansky’s notions of transitivity and full transitivity, Quart. J. Math. Oxford, 27, 15-20 (1976) · Zbl 0326.20046 · doi:10.1093/qmath/27.1.15
[51] Corner, ALS, Fully rigid systems of modules, Rend. Sem. Mat. Univ. Padova, 82, 55-66 (1989) · Zbl 0712.16007
[52] Corner, ALS; Göbel, R., Prescribing endomorphism algebras, a unified treatment, Proc. London Math. Soc., 50, 3, 447-479 (1985) · Zbl 0562.20030 · doi:10.1112/plms/s3-50.3.447
[53] A. L. S. Corner and B. Goldsmith, “Isomorphic automorphism groups of torsion-free p-adic modules,” in: Abelian Groups, Theory of Modules, and Topology, Marcel Dekker, New York (1998), pp. 125-130. · Zbl 0943.13018
[54] P. Crawley and A. W. Hales paper The structure of torsion Abelian groups given by presentations Bull. Am. Math. Soc., 74, 954-956 (1968). · Zbl 0194.04502
[55] Crawley, P.; Hales, AW, The structure of Abelian p-groups given by certain presentations, J. Algebra, 12, 10-23 (1969) · Zbl 0174.31103 · doi:10.1016/0021-8693(69)90014-3
[56] Crawley, P.; Jónsson, B., Refinements for infinite direct decompositions of algebraic systems, Pac. J. Math., 14, 797-855 (1964) · Zbl 0134.25504 · doi:10.2140/pjm.1964.14.797
[57] Davydova, OI, Rank-1 quotient divisible groups, Fundam. Prikl. Mat., 13, 3, 25-33 (2007)
[58] Yu. B. Dobrusin, Abelian groups close to algebraically compact groups [in Russian], thesis, Tomsk (1981).
[59] Dugas, M., On the existence of large mixed modules, Lect. Notes Math., 1006, 412-424 (1983) · Zbl 0525.20038 · doi:10.1007/978-3-662-21560-9_25
[60] Dugas, M., On the Jacobson radical of some endomorphism rings, Proc. Am. Math. Soc., 102, 4, 823-826 (1988) · Zbl 0651.20057 · doi:10.1090/S0002-9939-1988-0934850-4
[61] Dugas, M., AA-rings, Commun. Algebra, 32, 10, 3853-3860 (2004) · Zbl 1069.20051 · doi:10.1081/AGB-200027758
[62] Dugas, M.; Feigelstock, S., A-rings, Colloq. Math., 96, 2, 277-292 (2003) · Zbl 1037.16021 · doi:10.4064/cm96-2-10
[63] Dugas, M.; Göbel, R., Every cotorsion-free ring is an endomorphism ring, Proc. London Math. Soc., 45, 319-336 (1982) · Zbl 0506.16022 · doi:10.1112/plms/s3-45.2.319
[64] Dugas, M.; Göbel, R., Every cotorsion-free algebra is an endomorphism algebra, Math. Z., 181, 451-470 (1982) · Zbl 0501.16031 · doi:10.1007/BF01182384
[65] Dugas, M.; Göbel, R., On endomorphism rings of primary Abelian groups, Math. Ann., 261, 359-385 (1982) · Zbl 0492.20035 · doi:10.1007/BF01455456
[66] Dugas, M.; Göbel, R., Endomorphism algebras of torsion modules, II, Lect. Notes Math., 1006, 400-411 (1983) · Zbl 0519.20038 · doi:10.1007/978-3-662-21560-9_24
[67] Dugas, M.; Göbel, R., Torsion-free Abelian groups with prescribed finitely topologized endomorphism rings, Proc. Am. Math. Soc., 90, 4, 519-527 (1984) · Zbl 0546.20047 · doi:10.1090/S0002-9939-1984-0733399-8
[68] Dugas, M.; Göbel, R.; Goldsmith, B., Representation of algebras over a complete discrete valuation ring, Quart. J. Math., 35, 2, 131-146 (1984) · Zbl 0536.16031 · doi:10.1093/qmath/35.2.131
[69] Dugas, M.; Vinsonhaler, C., Two-side E-rings, J. Pure Appl. Algebra, 185, 87-102 (2003) · Zbl 1034.20048 · doi:10.1016/S0022-4049(03)00090-2
[70] Eklof, PC, Set-Theoretic Methods in Homological Algebra and Abelian Groups, Presses Univ (1980), Montréal: Montréal, Montréal · Zbl 0488.03029
[71] Eklof, PC; Goodearl, KR; Trlifaj, J., Dually slender modules and steady rings, Forum. Math., 9, 1, 61-74 (1997) · Zbl 0866.16003
[72] Eklof, PC; Mekler, AH, Almost Free Modules (1990), North-Holland, Amsterdam: Set-Theoretic Methods, North-Holland, Amsterdam · Zbl 0718.20027
[73] Eraskina, AP, On the λ-purity of modules over discrete valuation rings, Sib. Mat. Zh., 14, 208-212 (1973) · Zbl 0265.13005 · doi:10.1007/BF00967276
[74] A. Facchini, Module Theory: Endomorphism Rings and Direct Sum Decompositions in Some Classes of Modules, Birkhäuser, Basel-Boston-Berlin (1998). · Zbl 0930.16001
[75] Facchini, A.; Zanardo, P., Discrete valuation domains and rank of their maximal extensions, Rend. Sem. Mat. Univ. Padova, 75, 143-156 (1986) · Zbl 0608.13010
[76] Faith, C., Algebra: Rings, Modules, and Categories (1973), Berlin: Springer-Verlag, Berlin · Zbl 0266.16001 · doi:10.1007/978-3-642-80634-6
[77] C. Faith, Algebra, Ring Theory, Springer-Verlag, Berlin (1976). · Zbl 0335.16002
[78] Faticoni, T., Categories of modules over endomorphism rings, Mem. Am. Math. Soc., 103, 492, 1-140 (1993) · Zbl 0773.16010
[79] Faticoni, TG, Direct sums and refinement, Commun. Algebra, 27, 1, 451-464 (1999) · Zbl 0920.20045 · doi:10.1080/00927879908826441
[80] Feigelstock, S., Full subrings of E-rings, Bull. Austr. Math. Soc., 54, 275-280 (1996) · Zbl 0861.16023 · doi:10.1017/S0004972700017731
[81] Feigelstock, S., Additive groups of commutative rings, Quaest. Math., 23, 2, 241-245 (2000) · Zbl 0971.20033 · doi:10.2989/16073600009485973
[82] S. Feigelstock, J. Hausen, and R. Raphael, “Groups which map onto their endomorphism rings,” in: Proc. Dublin Conf. 1998, Basel (1999), pp. 231-241. · Zbl 0937.20031
[83] Files, ST, Mixed modules over incomplete discrete valuation rings, Commun. Algebra, 21, 11, 4103-4113 (1993) · Zbl 0790.13003 · doi:10.1080/00927879308824786
[84] Files, ST, Endomorphisms of local Warfield groups, Contemp. Math., 171, 99-107 (1994) · Zbl 0822.20057 · doi:10.1090/conm/171/01766
[85] Files, ST, Outer automorphisms of endomorphism rings of Warfield groups, Arch. Math., 65, 15-22 (1995) · Zbl 0823.20059 · doi:10.1007/BF01196573
[86] Files, ST, Endomorphism algebras of modules with distinguished torsion-free elements, J. Algebra, 178, 264-276 (1995) · Zbl 0859.13004 · doi:10.1006/jabr.1995.1348
[87] Files, ST, On transitive mixed Abelian groups, Lect. Notes Pure Appl. Math., 132, 243-251 (1996) · Zbl 0870.20039
[88] Files, ST, Transitivity and full transitivity for nontorsion modules, J. Algebra, 197, 468-478 (1997) · Zbl 0890.20039 · doi:10.1006/jabr.1997.7062
[89] Files, ST, The fully invariant subgroups of local Warfield groups, Proc. Am. Math. Soc., 125, 12, 3515-3518 (1997) · Zbl 0890.20040 · doi:10.1090/S0002-9939-97-03999-3
[90] Files, ST; Goldsmith, B., Transitive and fully transitive groups, Proc. Am. Math. Soc., 126, 6, 1605-1610 (1998) · Zbl 0909.20034 · doi:10.1090/S0002-9939-98-04330-5
[91] M. Flagg, “A Jacobson radical isomorphism theorem for torsion-free modules,” in: Models, Modules and Abelian Groups, de Gruyter, Berlin (2008), pp. 309-314. · Zbl 1196.20062
[92] Flagg, M., Jacobson radical isomorphism theorems for mixed modules part one: determining the torsion, Commun. Algebra, 37, 5, 1739-1747 (2009) · Zbl 1206.20063 · doi:10.1080/00927870802210613
[93] Flagg, M., The role of the Jacobson radical in isomorphism theorems, Contemp. Math., 576, 77-88 (2012) · Zbl 1264.20054 · doi:10.1090/conm/576/11350
[94] M. Flagg, “The Jacobson radical’s role in isomorphism theorems for p-adic modules extends to topogical isomorphism,” in: Groups, Modules, and Model Theory Surveys and Resent Developments, Springer-Verlag (2017), pp. 285-300. · Zbl 1436.16021
[95] Fomin, AA, Abelian groups with free subgroups of infinite index and their endomorphism groups, Mat. Zametki, 36, 2, 179-187 (1984) · Zbl 0571.20047
[96] Fomin, AA, Duality in some classes of Abelian torsion-free groups of finite rank, Sib. Mat. Zh., 27, 4, 117-127 (1986) · Zbl 0633.20031
[97] A. A. Fomin, “Pure free groups,” in: Abelian Groups and Modules [in Russian], 6, Tomsk (1986), pp. 145-164.
[98] Fomin, AA, Invariants and duality in some classes of Abeliantorsion-free groups of finite rank, Algebra Logika, 26, 1, 63-83 (1987) · Zbl 0655.20034 · doi:10.1007/BF01978383
[99] Fomin, AA, The category of quasi-homomorphisms of torsion-free Abelian groups of finite rank, Contemp. Math., 131, 91-111 (1992) · Zbl 0774.20033 · doi:10.1090/conm/131.1/1175765
[100] Fomin, AA, Finitely presented modules over the ring of universal numbers, Contemp. Math., 171, 109-120 (1994) · Zbl 0835.20074 · doi:10.1090/conm/171/01767
[101] A. A. Fomin and W. Wickless, “Categories of mixed and torsion-free Abelian groups,” in: Abelian Groups and Modules, Kluwer, Boston (1995), pp. 185-192. · Zbl 0844.20036
[102] Fomin, AA; Wickless, W., Quotient divisible Abelian groups, Proc. Am. Math. Soc., 126, 1, 45-52 (1998) · Zbl 0893.20041 · doi:10.1090/S0002-9939-98-04230-0
[103] Franzen, B.; Göbel, R., Prescribing endomorphism algebras, the cotorsion-free case, Rend. Sem. Mat. Univ. Padova, 80, 215-241 (1989) · Zbl 0673.16021
[104] Franzen, B.; Goldsmith, B., On endomorphism algebras of mixed modules, J. London Math. Soc., 31, 3, 468-472 (1985) · Zbl 0571.20051 · doi:10.1112/jlms/s2-31.3.468
[105] Franzsen, WN; Schultz, P., The endomorphism ring of locally free module, J. Austr. Math. Soc. Ser. A., 35, 308-326 (1983) · Zbl 0523.16023 · doi:10.1017/S1446788700027002
[106] Friger, MD, On torsion-free rigid rings, Sib. Mat. Zh., 27, 3, 217-219 (1986) · Zbl 0603.16015
[107] Fuchs, L., On the structure of Abelian p-groups, Acta Math. Acad. Sci. Hung., 4, 267-288 (1953) · Zbl 0052.02203 · doi:10.1007/BF02127586
[108] Fuchs, L., Notes on Abelian groups, I, Ann. Univ. Sci. Budapest., 2, 5-23 (1959) · Zbl 0090.02001
[109] Fuchs, L., Notes on Abelian groups, II, Acta Math. Acad. Sci. Hung., 11, 117-125 (1960) · Zbl 0090.02002 · doi:10.1007/BF02020629
[110] L. Fuchs, Infinite Abelian Groups. Vols. I, II, Academic Press, New York-London (1970, 1973). · Zbl 0209.05503
[111] Fuchs, L., Abelian p-Groups and Mixed Groups, Univ (1980), Montreal: Montreal Press, Montreal · Zbl 0455.20037
[112] L. Fuchs, Abelian Groups, Springer-Verlag (2015). · Zbl 1416.20001
[113] L. Fuchs and L. Salce, “Modules over valuation domains,” in: Lect. Notes Pure Appl. Math, 97, Marcel Dekker, New York (1985). · Zbl 0578.13004
[114] L. Fuchs and L. Salce, “Modules over non-Noetherian domains,”, Math. Surv. Monogr., 84, Am. Math. Soc., Providence, Rhode Island (2001). · Zbl 0973.13001
[115] Gabriel, P., Des catégories abéliennes, Bull. Soc. Math. Fr., 90, 323-448 (1962) · Zbl 0201.35602 · doi:10.24033/bsmf.1583
[116] Goeters, HP, The structure of Ext for torsion-free modules of finite rank over Dedekind domains, Commun. Algebra, 31, 7, 3251-3263 (2003) · Zbl 1079.13010 · doi:10.1081/AGB-120022222
[117] Goldsmith, B., Endomorphism rings of torsion-free modules over a complete discrete valuation ring, J. London Math. Soc., 2, 3, 464-471 (1978) · Zbl 0394.16024 · doi:10.1112/jlms/s2-18.3.464
[118] B. Goldsmith, “Essentially-rigid families of Abelian p-groups,” J. London Math. Soc. (2), 18, 70-74 (1978). · Zbl 0389.20045
[119] Goldsmith, B., Essentially indecomposable modules over a complete discrete valuation ring, Rend. Sem. Mat. Univ. Padova, 70, 21-29 (1983) · Zbl 0581.13009
[120] B. Goldsmith, “An essentially semi-rigid class of modules,” J. London Math. Soc. (2), 29, No. 3, 415-417 (1984). · Zbl 0559.13006
[121] B. Goldsmith, “On endomorphisms and automorphisms of some torsion-free modules,” in: Abelian Group Theory, Gordon and Breach, New York (1987), pp. 417-423. · Zbl 0661.20036
[122] Goldsmith, B., On endomorphism rings of non-separable Abelian p-groups, J. Algebra, 127, 73-79 (1989) · Zbl 0687.20050 · doi:10.1016/0021-8693(89)90274-3
[123] Goldsmith, B.; May, W., The Krull-Schmidt problem for modules over valuation domains, J. Pure Appl. Algebra, 140, 1, 57-63 (1999) · Zbl 0987.13012 · doi:10.1016/S0022-4049(98)00012-7
[124] Goldsmith, B.; Pabst, S.; Scott, A., Unit sum numbers of rings and modules, Quart. J. Math., 49, 331-344 (1998) · Zbl 0933.16035 · doi:10.1093/qmathj/49.3.331
[125] Goldsmith, B.; Zanardo, P., On the analogue of Corner’s finite rank theorem for modules over valuation domains, Arch. Math., 60, 1, 20-24 (1993) · Zbl 0793.20052 · doi:10.1007/BF01194234
[126] Goldsmith, B.; Zanardo, P., The Walker endomorphism algebra of a mixed module, Proc. Roy. Irish Acad. Sect. A, 93, 1, 131-136 (1993) · Zbl 0802.16021
[127] B. Goldsmith and P. Zanardo, “Endomorphism rings and automorphism groups of separable torsion-free modules over valuation domains,” in: Abelian Groups, Theory of Modules, and Topology, Marcel Dekker, New York (1998), pp. 249-260. · Zbl 0934.13006
[128] Goodearl, KR, Ring Theory (1976), New York-Basel: Marcel Dekker, New York-Basel · Zbl 0336.16001
[129] Göbel, R., Endomorphism rings of Abelian groups, Lect. Notes Math., 1006, 340-353 (1983) · Zbl 0516.20032 · doi:10.1007/978-3-662-21560-9_17
[130] R. Göbel, “Modules with distinguished submodules and their endomorphism algebras,” in: Abelian Groups, Marcel Dekker, New York (1993), pp. 55-64. · Zbl 0811.16022
[131] R. Göbel and B. Goldsmith, “Essentially indecomposable modules which are almost free,” Quart. J. Math. Oxford (2), 39, 213-222 (1988). · Zbl 0675.13010
[132] Göbel, R.; Goldsmith, B., Mixed modules in L, Rocky Mountain J. Math., 19, 1043-1058 (1989) · Zbl 0697.20046 · doi:10.1216/RMJ-1989-19-4-1043
[133] Göbel, R.; Goldsmith, B., On almost-free modules over complete discrete valuation rings, Rend. Sem. Mat. Univ. Padova, 86, 75-87 (1991) · Zbl 0756.13015
[134] Göbel, R.; Goldsmith, B., On separable torsion-free modules of countable density character, J. Algebra, 144, 79-87 (1991) · Zbl 0737.20026 · doi:10.1016/0021-8693(91)90128-U
[135] Göbel, R.; Goldsmith, B., Cotorsion-free algebras as endomorphism algebras in L — the discrete and topological cases, Comment. Math. Univ. Carol., 34, 1, 1-9 (1993) · Zbl 0804.16031
[136] Göbel, R.; May, W., The construction of mixed modules from torsion modules, Arch. Math., 48, 476-490 (1987) · Zbl 0624.13011 · doi:10.1007/BF01190354
[137] Göbel, R.; May, W., Independence in completions and endomorphism algebras, Forum Math., 1, 215-226 (1989) · Zbl 0691.13004 · doi:10.1515/form.1989.1.215
[138] Göbel, R.; Opdenhövel, A., Every endomorphism of a local Warfield module of finite torsionfree rank is the sum of two automorphisms, J. Algebra, 233, 758-771 (2000) · Zbl 1057.20040 · doi:10.1006/jabr.2000.8378
[139] Göbel, R.; Paras, A., Splitting off free summand of torsion-free modules over complete dvrs, Glasgow Math. J., 44, 349-351 (2002) · Zbl 1068.13005 · doi:10.1017/S0017089502020177
[140] R. Göbel, S. Shelah, and L. Strüngmann, “Generalized E-Rings,” arXiv.org/pdf/math/0404271 (2003). · Zbl 1044.20035
[141] Göbel, R.; Shelah, S.; Strüngmann, L., ℵ_n-Free modules over complete discrete valuation domains with almost trivial duals, Glasgow Math. J., 55, 369-380 (2013) · Zbl 1272.13009 · doi:10.1017/S0017089512000614
[142] R. Göbel and J. Trlifaj, “Approximations and Endomorphism Algebras of Modules,”, Expos. Math., 41, de Gruyter, Berlin (2006). · Zbl 1121.16002
[143] Göbel, R.; Wald, B., Separable torsion-free modules of small type, Houston J. Math., 16, 271-287 (1990) · Zbl 0733.13009
[144] Grätzer, G., General Lattice Theory (1978), Berlin: Academie-Verlag, Berlin · Zbl 0385.06014 · doi:10.1007/978-3-0348-7633-9
[145] Griffith, P., Transitive and fully transitive primary Abelian groups, Pac. J. Math., 25, 249-254 (1968) · Zbl 0157.05901 · doi:10.2140/pjm.1968.25.249
[146] P. A. Griffith, Infinite Abelian Group Theory, Univ. of Chicago Press, Chicago-London (1970). · Zbl 0204.35001
[147] Grinshpon, SY, Fully invariant subgroups of separable Abelian groups, Fundam. Prikl. Mat., 4, 4, 1279-1305 (1998) · Zbl 0951.20041
[148] Grinshpon, SY, Fully invariant subgroups of torsion free Abelian groups and their lattices, Fundam. Prikl. Mat., 6, 3, 739-751 (2000) · Zbl 0993.20033
[149] S. Ya. Grinshpon, Fully invariant subgroups of Abelian groups and full transitivity [in Russian], thesis, Tomsk (2000). · Zbl 1026.20034
[150] Grinshpon, SY, Fully invariant subgroups of Abelian groups and full transitivity, Fundam. Prikl. Mat., 8, 2, 407-473 (2002) · Zbl 1026.20034
[151] Grinshpon, SY; Krylov, PA, Fully invariant subgroups, full transitivity, and homomorphism groups of Abelian groups, J. Math. Sci., 128, 3, 2894-2997 (2005) · Zbl 1131.20041 · doi:10.1007/s10958-005-0245-5
[152] S. Ya. Grinshpon and V. M. Misyakov, “On fully transitive Abelian groups,” in: Abelian Groups and Modules [in Russian], 6, Tomsk (1986), pp. 12-27. · Zbl 0753.20016
[153] Grishin, AV, Strongly indecomposable localizations of the ring of algebraic integers, Commun. Algebra, 43, 9, 3816-3822 (2015) · Zbl 1331.11090 · doi:10.1080/00927872.2014.896374
[154] Grishin, AV; Tsarev, AV, Ɛ-closed groups and modules, J. Math. Sci. (New York), 186, 4, 592-598 (2012) · Zbl 1272.20058 · doi:10.1007/s10958-012-1008-8
[155] Gubareni, N., Valuation and discrete valuation rings, Sci. Res. Inst. Math. Comp. Sci., 10, 1, 61-70 (2011)
[156] Harada, M., Factor Categories with Applications to Direct Decomposition of Modules (1983), New York: Marcel Dekker, New York · Zbl 0526.16001
[157] Harrison, DK, Infinite Abelian groups and homological methods, Ann. Math., 69, 2, 366-391 (1959) · Zbl 0100.02901 · doi:10.2307/1970188
[158] D. K. Harrison, “On the structure of Ext,” in: Topics in Abelian Groups, Scott Foresman and Co., Chicago (1963), pp. 195-209.
[159] Hausen, J., Modules with the summand intersection property, Commun. Algebra, 17, 1, 135-148 (1989) · Zbl 0667.16020 · doi:10.1080/00927878908823718
[160] Hausen, J.; Johnson, JA, Determining Abelian p-groups by the Jacobson radical of their endomorphism rings, J. Algebra, 174, 217-224 (1995) · Zbl 0837.20067 · doi:10.1006/jabr.1995.1125
[161] Hausen, J.; Praeger, CE; Schultz, P., Most Abelian p-groups are determined by the Jacobson radical of their endomorphism rings, Math. Z., 216, 431-436 (1994) · Zbl 0811.20046 · doi:10.1007/BF02572332
[162] Hennecke, G.; Strüngmann, L., Transitivity and full transitivity for p-local modules, Arch. Math., 74, 321-329 (2000) · Zbl 0963.13019 · doi:10.1007/s000130050450
[163] Herstein, IN, Noncommutative Rings (1968), New York: Wiley, New York · Zbl 0177.05801
[164] Hill, P., Sums of countable primary groups, Proc. Am. Math. Soc., 17, 1469-1470 (1966) · Zbl 0158.27405
[165] Hill, P., Ulm’s theorem for totally projective groups, Not. Am. Math. Soc., 14, 940 (1967)
[166] Hill, P., On transitive and fully transitive primary groups, Proc. Am. Math. Soc., 22, 414-417 (1969) · Zbl 0192.35601 · doi:10.1090/S0002-9939-1969-0269735-0
[167] Hill, P., Endomorphism rings generated by units, Trans. Am. Math. Soc., 141, 99-105 (1969) · Zbl 0192.35603 · doi:10.1090/S0002-9947-1969-0242944-7
[168] P. Hill, “The classification problem,” in: Abelian Groups and Modules, Springer-Verlag, Vienna (1984), pp. 1-16. · Zbl 0573.20052
[169] P. Hill, M. Lane, and . Megibben, “On the structure of p-local groups,” J. Algebra, 143, 29-45 (1991). · Zbl 0752.20027
[170] Hill, P.; Megibben, C., On the theory and classification of Abelian p-groups, Math. Z., 190, 17-38 (1985) · Zbl 0535.20031 · doi:10.1007/BF01159160
[171] Hill, P.; Megibben, C., Axiom 3 modules, Trans. Am. Math. Soc., 295, 2, 715-734 (1986) · Zbl 0597.20048
[172] Hill, P.; Megibben, C., Torsion-free groups, Trans. Am. Math. Soc., 295, 735-751 (1986) · Zbl 0597.20047 · doi:10.1090/S0002-9947-1986-0833706-8
[173] Hill, P.; Megibben, C., Mixed groups, Trans. Am. Math. Soc., 334, 121-142 (1992) · Zbl 0798.20050 · doi:10.1090/S0002-9947-1992-1116315-8
[174] Hill, P.; Ullery, W., The transitivity of local Warfied groups, J. Algebra, 208, 643-661 (1998) · Zbl 0916.20039 · doi:10.1006/jabr.1998.7539
[175] Hill, P.; Ullery, W., Isotype subgroups of local Warfield groups, Commun. Algebra, 29, 5, 1899-1907 (2001) · Zbl 0996.20036 · doi:10.1081/AGB-100002156
[176] Hill, P.; West, JK, Subgroup transitivity in Abelian groups, Proc. Am. Math. Soc., 126, 5, 1293-1303 (1998) · Zbl 0898.20032 · doi:10.1090/S0002-9939-98-04234-8
[177] Hunter, R., Balanced subgroups of Abelian groups, Trans. Am. Math. Soc., 215, 81-98 (1976) · Zbl 0321.20035 · doi:10.1090/S0002-9947-1976-0507068-3
[178] Hunter, R.; Richman, F., Global Warfield groups, Trans. Am. Math. Soc., 266, 1, 555-572 (1981) · Zbl 0471.20038 · doi:10.1090/S0002-9947-1981-0617551-X
[179] Hunter, R.; Richman, F.; Walker, E., Warfield modules, Lect. Notes Math., 616, 87-123 (1977) · Zbl 0376.13007 · doi:10.1007/BFb0068191
[180] Hunter, R.; Richman, F.; Walker, E., Existence theorems for Warfield groups, Trans. Am. Math. Soc., 235, 345-362 (1978) · Zbl 0368.20034 · doi:10.1090/S0002-9947-1978-0473044-4
[181] Hunter, R.; Walker, E., S-groups revisited, Proc. Am. Math. Soc., 82, 13-18 (1981) · Zbl 0464.20037
[182] Irwan, SE; Garminia, H.; Astuti, P., On valuations of vector spaces, JP J. Alg. Number Theory Appl., 38, 6, 633-646 (2016) · Zbl 1362.13006
[183] A. V. Ivanov, “On a problem of Abelian groups,” Mat. Sb., 105 (147), No. 4, 525-542 (1978). · Zbl 0386.20031
[184] A. Jaballah, “Integral domains whose overrings are dicrete valuation rings,” An. Stiint. Univ. Al. I. Cuza Iasi Mat. (N.S.), 62, No. 2, 361-369 (2016). · Zbl 1389.13022
[185] Jacobson, N., Structure of Rings (1968), Providence, Rhode Island: Am. Math. Soc, Providence, Rhode Island · Zbl 0218.17010
[186] Jarisch, R.; Mutzbauer, O.; Toubassi, E., Calculating indicators in a class of mixed modules, Lect. Notes Pure Appl. Math., 182, 291-301 (1996) · Zbl 0883.13010
[187] Jarisch, R.; Mutzbauer, O.; Toubassi, E., Characterizing a class of simply presented modules by relation arrays, Arch. Math., 71, 349-357 (1998) · Zbl 0955.13002 · doi:10.1007/s000130050276
[188] Jarisch, R.; Mutzbauer, O.; Toubassi, E., Characterizing a class of Warfield modules by relation arrays, Rocky Mountain J. Math., 30, 4, 1293-1314 (2000) · Zbl 1001.20047 · doi:10.1216/rmjm/1021477352
[189] Jarisch, R.; Mutzbauer, O.; Toubassi, E., Characterizing a class of Warfield modules by Ulm submodules and Ulm factors, Arch. Math., 76, 326-336 (2001) · Zbl 0984.20032 · doi:10.1007/PL00000440
[190] Jech, T., Set Theory (1978), New York: Academic Press, New York · Zbl 0419.03028
[191] I. Kaplansky, Infinite Abelian Groups, Univ. of Michigan Press (1954). · Zbl 0057.01901
[192] Kaplansky, I., Projective modules, Ann. Math., 68, 372-377 (1958) · Zbl 0083.25802 · doi:10.2307/1970252
[193] Kaplansky, I., Modules over Dedekind rings and valuation rings, Trans. Am. Math. Soc., 72, 327-340 (1952) · Zbl 0046.25701 · doi:10.1090/S0002-9947-1952-0046349-0
[194] Kaplansky, I.; Mackey, G., A generalization of Ulm’s theorem, Summa Brasil. Math., 2, 195-202 (1951) · Zbl 0054.01803
[195] Kasch, F., Modules and Rings (1982), London-New York: Academic Press, London-New York · Zbl 0523.16001
[196] Keef, P., An equivalence for categories of modules over a complete discrete valuation domain, Rocky Mountain J. Math., 27, 3, 843-860 (1997) · Zbl 0916.13009 · doi:10.1216/rmjm/1181071897
[197] Kolettis, G. Jr, Direct sums of countable groups, Duke Math. J., 27, 111-125 (1960) · Zbl 0091.02802 · doi:10.1215/S0012-7094-60-02711-3
[198] Krylov, PA, Strongly homogeneous torsion-free abelian groups, Sib. Mat. Zh., 24, 2, 77-84 (1983) · Zbl 0536.20038 · doi:10.1007/BF00968737
[199] Krylov, PA, Fully transitive torsion-free Abelian groups, Algebra Logika, 29, 5, 549-560 (1990) · Zbl 0739.20025 · doi:10.1007/BF02215284
[200] P. A. Krylov, Endomorphism rings and structural theory of abelian groups [in Russian], thesis, Tomsk (1991).
[201] Krylov, PA, Mixed Abelian groups as modules over their endomorphism rings, Fundam. Prikl. Mat., 6, 3, 793-812 (2000) · Zbl 1019.20023
[202] Krylov, PA, Affine module groups and their automorphisms, Algebra Logika, 40, 1, 60-82 (2001) · Zbl 0979.20044 · doi:10.1023/A:1002802222089
[203] Krylov, PA, Hereditary endomorphism rings of mixed Abelian groups, Sib. Mat. Zh., 43, 1, 108-119 (2002) · Zbl 1013.20052 · doi:10.1023/A:1013876621908
[204] Krylov, PA, Jacobson radical of the endomorphism ring of an Abelian group, Algebra Logika, 43, 1, 60-76 (2004) · Zbl 1065.20066 · doi:10.1023/B:ALLO.0000015129.15394.33
[205] Krylov, PA; Chekhlov, AR, Torsion-free Abelian groups with a large number of endomorphisms, Tr. Inst. Mat. Mekh. Ural. Otdel. Ross. Akad. Nauk, 7, 2, 194-207 (2001) · Zbl 1121.20311
[206] Krylov, PA; Klassen, ED, The center of the endomorphism ring of a splitting mixed Abelian group, Sib. Mat. Zh., 40, 5, 1074-1085 (1999) · Zbl 0936.20043 · doi:10.1007/BF02674720
[207] Krylov, PA; Mikhalev, AV; Tuganbaev, AA, Endomorphism rings of Abelian groups, J. Math. Sci., 110, 3, 2683-2745 (2002) · Zbl 1017.20047 · doi:10.1023/A:1015190932351
[208] Krylov, PA; Mikhalev, AV; Tuganbaev, AA, Endomorphism Rings of Abelian Groups (2003), Dordrecht-Boston-London: Kluwer Academic Publishers, Dordrecht-Boston-London · Zbl 1044.20037 · doi:10.1007/978-94-017-0345-1
[209] Krylov, PA; Pakhomova, EG, Abelian groups and regular modules, Mat. Zametki, 69, 3, 402-411 (2001) · Zbl 1004.20035 · doi:10.4213/mzm513
[210] Krylov, PA; Tuganbaev, AA, Modules over discrete valuation domains, I, J. Math. Sci., 145, 4, 4997-5117 (2007) · Zbl 1178.13012 · doi:10.1007/s10958-007-0335-7
[211] Krylov, PA; Tuganbaev, AA, Modules over discrete valuation domains, II, J. Math. Sci., 151, 5, 3255-3371 (2008) · Zbl 1229.13018 · doi:10.1007/s10958-008-9039-x
[212] Krylov, PA; Tuganbaev, AA, Idempotent functors and localizations in the categories of modules and abelian groups, Fundam. Prikl. Mat., 16, 7, 75-159 (2010)
[213] P. A. Krylov and A. A. Tuganbaev, Formal Matrices, Springer-Verlag (2017). · Zbl 1367.16001
[214] Krylov, PA; Tuganbaev, AA; Tsarev, AV, Around the Baer-Kaplansky theorem, Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 159, 46-67 (2019) · Zbl 1487.16002
[215] L. Ya. Kulikov, “On the theory of Abelian groups of arbitrary cardinality,” Mat. Sb., 9 (51), No. 1, 165-181 (1941). · Zbl 0025.29901
[216] L. Ya. Kulikov, “On the theory of Abelian groups of arbitrary cardinality,” Mat. Sb., 16 (58), No. 2, 129-162 (1945). · Zbl 0061.03410
[217] L. Ya. Kulikov, “Generalized primary groups, I,” Tr. Mosk. Mat. Obshch., 1, 247-326 (1952). · Zbl 0053.21001
[218] L. Ya. Kulikov, “Generalized primary groups, II,” Tr. Mosk. Mat. Obshch., 2, 85-167 (1953). · Zbl 0053.21001
[219] Kurosh, AG, Primitive torsionsfreie abelsche gruppen vom endlichen range, Ann. Math., 38, 175-203 (1937) · JFM 63.0074.01 · doi:10.2307/1968518
[220] Kurosh, AG, The Theory of Groups (1960), New York: Chelsea Publ, New York · Zbl 0094.24501
[221] Lady, EL, On classifying torsion free modules over discrete valuation rings, Lect. Notes Math., 616, 168-172 (1977) · Zbl 0375.13002 · doi:10.1007/BFb0068195
[222] Lady, EL, Splitting fields for torsion-free modules over discrete valuation rings, I, J. Algebra, 49, 261-275 (1977) · Zbl 0366.13002 · doi:10.1016/0021-8693(77)90285-X
[223] Lady, EL, Splitting fields for torsion-free modules over discrete valuation rings, II, J. Algebra, 66, 281-306 (1980) · Zbl 0455.13003 · doi:10.1016/0021-8693(80)90124-6
[224] Lady, EL, Splitting fields for torsion-free modules over discrete valuation rings, III, J. Algebra, 66, 307-320 (1980) · Zbl 0455.13004 · doi:10.1016/0021-8693(80)90125-8
[225] Lam, TY, A First Cource in Noncommutative Rings (1991), New York: Springer-Verlag, New York · Zbl 0728.16001 · doi:10.1007/978-1-4684-0406-7
[226] Lambek, J., Lecture on Rings and Modules (1968), Waltham: Blaisdell Publ, Waltham · Zbl 0176.28901
[227] Lane, M., A new charterization for p-local balanced projective groups, Proc. Am. Math. Soc., 96, 379-386 (1986) · Zbl 0594.20049
[228] Lane, M., Isotype submodules of p-local balanced projective groups, Trans. Am. Math. Soc., 301, 1, 313-325 (1987) · Zbl 0619.20036
[229] Lane, M., Fully invariant submodules of p-local balanced projective groups, Rocky Mountain J. Math., 18, 4, 833-841 (1988) · Zbl 0693.20049 · doi:10.1216/RMJ-1988-18-4-833
[230] Lane, M.; Megibben, C., Balance projectives and Axiom 3, J. Algebra, 111, 457-474 (1987) · Zbl 0629.20025 · doi:10.1016/0021-8693(87)90230-4
[231] Leptin, H., Abelsche p-gruppen und ihre Automorphismengruppen, Math. Z., 73, 235-253 (1960) · Zbl 0093.24802 · doi:10.1007/BF01159715
[232] Levy, L., Torsion-free and divisible modules over non-integral domains, Can. J. Math., 15, 1, 132-151 (1963) · Zbl 0108.04001 · doi:10.4153/CJM-1963-016-1
[233] W. Liebert, “Endomorphism rings of Abelian p-groups,” in: Études sur les Groupes Abéliens, Springer-Verlag, Berlin (1968), pp. 239-258. · Zbl 0185.06201
[234] Liebert, W., Characterization of the endomorphism rings of divisible torsion modules and reduced complete torsion-free modules over complete discrete valuation rings, Pac. J. Math., 37, 1, 141-170 (1971) · Zbl 0214.05704 · doi:10.2140/pjm.1971.37.141
[235] Liebert, W., Endomorphism rings of reduced torsion-free modules over complete discrete valuation rings, Trans. Am. Math. Soc., 169, 347-363 (1972) · Zbl 0282.16016 · doi:10.1090/S0002-9947-1972-0306268-1
[236] Liebert, W., Endomorphism rings of reduced complete torsion-free module over complete discrete valuation rings, Proc. Am. Math. Soc., 36, 1, 375-378 (1972) · Zbl 0226.16030 · doi:10.1090/S0002-9939-1972-0310019-X
[237] W. Liebert, “The Jacobson radical of some endomorphism rings,” J. Reine Angew. Math., 262/263, 166-170 (1973). · Zbl 0266.16004
[238] Liebert, W., On-sided ideals in the endomorphism rings of reduced complete torsion-free modules and divisible torsion modules over complete discrete valuation rings, Symp. Math., 13, 273-298 (1974) · Zbl 0288.16012
[239] Liebert, W., Endomorphism rings of free modules over principal ideal domains, Duke Math. J., 41, 323-328 (1974) · Zbl 0283.16012 · doi:10.1215/S0012-7094-74-04136-2
[240] Liebert, W., Endomorphism rings of Abelian p-groups, Lect. Notes Math., 1006, 384-399 (1983) · Zbl 0531.20032 · doi:10.1007/978-3-662-21560-9_23
[241] W. Liebert, “Isomorphic automorphism groups of primary Abelian groups,” in: Abelian Group Theory, Gordon and Breach, New York (1987), pp. 9-31. · Zbl 0654.20063
[242] Loth, P., Classification of Abelian Groups and Pontryagin Duality (1998), Amsterdam: Gordon and Breach, Amsterdam · Zbl 1016.20038
[243] Loth, P., Characterizations of Warfield groups, J. Algebra, 204, 32-41 (1998) · Zbl 0909.20040 · doi:10.1006/jabr.1997.7367
[244] MacLane, S., Homology (1963), New York: Academic Press, New York · Zbl 0149.26203 · doi:10.1007/978-3-642-62029-4
[245] MacLane, S., Categories for the Working Mathematician (1971), Berlin: Springer-Verlag, Berlin · Zbl 0705.18001
[246] Mader, A., Almost Completely Decomposable Groups (1998), Amsterdam: Gordon & Breach, Amsterdam · Zbl 0912.20044
[247] Mader, A.; Vinsonhaler, C., Torsion-free E-modules, J. Algebra, 115, 2, 401-411 (1988) · Zbl 0639.13010 · doi:10.1016/0021-8693(88)90266-9
[248] Markov, VT; Mikhalev, AV; Skornyakov, LA; Tuganbaev, AA, Endomorphism rings of modules and submodule structures, Itogi Nauki Tekhn. Algebra. Topol. Geom., 21, 183-254 (1983) · Zbl 0566.16018
[249] E. Matlis, “Cotorsion modules,” Mem. Am. Math. Soc., 49 (1964). · Zbl 0135.07801
[250] Matlis, E., The decomposability of torsion-free modules of finite rank, Trans. Am. Math. Soc., 134, 2, 315-324 (1968) · Zbl 0184.06602 · doi:10.1090/S0002-9947-1968-0230757-0
[251] May, W., Endomorphism rings of mixed Abelian groups, Contemp. Math., 87, 61-74 (1989) · Zbl 0687.20051 · doi:10.1090/conm/087/995265
[252] May, W., Isomorphism of endomorphism algebras over complete discrete valuation rings, Math. Z., 204, 485-499 (1990) · Zbl 0681.13002 · doi:10.1007/BF02570888
[253] W. May, “Endomorphism algebras of not necessarily cotorsion-free modules,” in: Abelian Groups and Noncommutative Rings, Am. Math. Soc., Providence, Rhode Island (1992), pp. 257-264. · Zbl 0779.16012
[254] May, W., Endomorphisms over incomplete discrete valuation domains, Contemp. Math., 171, 277-285 (1994) · Zbl 0829.20078 · doi:10.1090/conm/171/01779
[255] May, W., The theorem of Baer and Kaplansky for mixed modules, J. Algebra, 177, 255-263 (1995) · Zbl 0840.16024 · doi:10.1006/jabr.1995.1297
[256] May, W., The use of the finite topology on endomorphism rings, J. Pure Appl. Algebra, 163, 107-117 (2001) · Zbl 0992.20040 · doi:10.1016/S0022-4049(00)00159-6
[257] May, W., Torsion-free modules with nearly unique endomorphism algebras, Commun. Algebra, 31, 3, 1271-1278 (2003) · Zbl 1014.13002 · doi:10.1081/AGB-120017766
[258] May, W.; Toubassi, E., Endomorphisms of rank one mixed modules over discrete valuation rings, Pac. J. Math., 108, 1, 155-163 (1983) · Zbl 0535.20034 · doi:10.2140/pjm.1983.108.155
[259] May, W.; Zanardo, P., Modules over domains large in a complete discrete valuation ring, Rocky Mountain J. Math., 30, 4, 1421-1436 (2000) · Zbl 0987.13002 · doi:10.1216/rmjm/1021477357
[260] Megibben, C., Large subgroups and small homomorphisms, Michigan Math. J., 13, 153-160 (1966) · Zbl 0166.02502 · doi:10.1307/mmj/1028999539
[261] Megibben, C., Modules over an incomplete discrete valuation ring, Proc. Am. Math. Soc., 19, 450-452 (1968) · Zbl 0163.28903 · doi:10.1090/S0002-9939-1968-0222071-X
[262] Megibben, C., A nontransitive, fully transitive primary group, J. Algebra, 13, 571-574 (1969) · Zbl 0208.03501 · doi:10.1016/0021-8693(69)90118-5
[263] van der Merwe, B., Unique addition modules, Commun. Algebra, 27, 9, 4103-4115 (1999) · Zbl 0945.16007 · doi:10.1080/00927879908826687
[264] A. V. Mikhalev, “Isomorphisms and anti-isomorphisms of endomorphism rings of modules,” in: First Int. Tainan-Moscow Algebra Workshop, Tainan, 1994, de Gruyter, Berlin (1996), pp. 69-122. · Zbl 0881.16017
[265] Mishina, AP; Skornyakov, LA, Abelian Groups and Modules (1976), Providence, Rhode Island: Am. Math. Soc, Providence, Rhode Island · Zbl 0331.13002
[266] V. M. Misyakov, Full transnativity of Abelian groups [in Russian], thesis, Tomsk (1992).
[267] Mo Bang, C., A classification of modules over complete discrete valuation rings, Bull. Am. Math. Soc., 76, 381-383 (1970) · Zbl 0214.29703
[268] Mo Bang, C., Countable generated modules over complete discrete valuation rings, J. Algebra, 14, 552-560 (1970) · Zbl 0203.05202 · doi:10.1016/0021-8693(70)90102-X
[269] Mo Bang, C., Direct sums of countable generated modules over complete discrete valuation rings, Proc. Am. Math. Soc., 28, 2, 381-388 (1971) · Zbl 0214.29704 · doi:10.1090/S0002-9939-1971-0276326-3
[270] Moghaderi, J.; Nekooei, R., Valuation, discrete valuation and Dedekind modules, Int. Electron. J. Algebra, 8, 18-29 (2010) · Zbl 1257.13002
[271] S. H. Mohamed and B. J. Muller, Continuous and Discrete Modules, Cambridge Univ. Press, Cambridge (1990). · Zbl 0701.16001
[272] Monk, G., One sided ideals in the endomorphism ring of an Abelian p-group, Acta Math. Acad. Sci., 19, 171-185 (1968) · Zbl 0157.35703 · doi:10.1007/BF01894692
[273] Moore, JH, A characterization of Warfield groups, Proc. Am. Math. Soc., 87, 617-620 (1983) · Zbl 0494.20034 · doi:10.1090/S0002-9939-1983-0687628-9
[274] Mutzbauer, O.; Toubassi, E., A splitting criterion for a class of mixed modules, Rocky Mountain J. Math., 24, 1533-1543 (1994) · Zbl 0836.13004 · doi:10.1216/rmjm/1181072355
[275] Mutzbauer, O.; Toubassi, E., Extending a splitting criterion on mixed modules, Contemp. Math., 171, 305-312 (1994) · Zbl 0842.20047 · doi:10.1090/conm/171/01782
[276] Mutzbauer, O.; Toubassi, E., Classification of mixed modules, Acta Math. Hung., 72, 1-2, 153-166 (1996) · Zbl 0854.13008 · doi:10.1007/BF00053703
[277] Nagata, M., Local Rings (1962), New York: Wiley, New York · Zbl 0123.03402
[278] Nunke, RJ, Modules of extensions over Dedekind rings, Ill. J. Math., 3, 222-241 (1959) · Zbl 0087.26603
[279] R. J. Nunke, “Purity and subfunctors of the identity,” in: Topics in Abelian Groups, Chicago-Illinois (1963), pp. 121-171.
[280] Nunke, RJ, Homology and direct sums of countable Abelian groups, Math. Z., 101, 182-212 (1967) · Zbl 0173.02401 · doi:10.1007/BF01135839
[281] R. S. Pierce, “Homomorphisms of primary Abelian groups,” in: Topics in Abelian Groups, Chicago, Illinois (1963), pp. 215-310.
[282] R. S. Pierce, “Endomorphism rings of primary Abelian groups,” in: Proc. Colloq. Abelian Groups, Académiai Kiadó, Budapest (1964), pp. 125-137. · Zbl 0131.02503
[283] R. S. Pierce, “E-modules,” in: Abelian group theory, Perth (1987), pp. 221-240. · Zbl 0674.20033
[284] Plotkin, BI, Groups of Automorphisms of Algebraic Systems (1972), Groningen: Wolters-Noordhoff Publ, Groningen · Zbl 0229.20004
[285] M. A. Prikhodovsky, Isomorphisms of tensor products of modules and T-modules [in Russian], thesis, Tomsk (2002).
[286] Procházka, L., A generalization of a Prüfer-Kaplansky theorem, Lect. Notes Math., 1006, 617-629 (1983) · Zbl 0533.13002 · doi:10.1007/978-3-662-21560-9_43
[287] Prüfer, H., Untersuchungen über die Zerlegbarkeit der abzählbaren primären Abelschen Gruppen, Math. Z., 17, 35-61 (1923) · JFM 49.0084.03 · doi:10.1007/BF01504333
[288] Puninsky, GE; Tuganbaev, AA, Ring and Modules [in Russian] (1998), Moscow: Soyuz, Moscow · Zbl 0941.16001
[289] Ribenboim, P., On the completion of a valuation ring, Math. Ann., 155, 392-396 (1964) · Zbl 0136.32102 · doi:10.1007/BF01350748
[290] Richman, F., The constructive theory of KT-modules, Pac. J. Math., 61, 621-637 (1975) · Zbl 0305.02046 · doi:10.2140/pjm.1975.61.263
[291] Richman, F., Mixed local groups, Lect. Notes Math., 874, 374-404 (1981) · Zbl 0459.20050 · doi:10.1007/BFb0090547
[292] Richman, F., Mixed groups, Lect. Notes Math., 1006, 445-470 (1983) · Zbl 0518.20050 · doi:10.1007/978-3-662-21560-9_28
[293] Richman, F., Nice subgroups of mixed local groups, Commun. Algebra, 11, 1, 1629-1642 (1983) · Zbl 0515.20038 · doi:10.1080/00927878308822924
[294] Richman, F.; Walker, EA, Extending Ulm’s theorem without group theory, Proc. Am. Math. Soc., 21, 194-196 (1969) · Zbl 0172.03202
[295] Richman, F.; Walker, EA, Filtered modules over discrete valuation domains, J. Algebra, 199, 2, 618-645 (1998) · Zbl 0904.13010 · doi:10.1006/jabr.1997.7217
[296] Rickart, CE, Isomorphic groups of linear transformations, Am. J. Math., 72, 451-464 (1950) · Zbl 0037.20101 · doi:10.2307/2372048
[297] Rotman, J., A note on completions of modules, Proc. Am. Math. Soc., 11, 356-360 (1960) · Zbl 0094.02304 · doi:10.1090/S0002-9939-1960-0114813-1
[298] Rotman, J., Mixed modules over valuation rings, Pac. J. Math., 10, 607-623 (1960) · Zbl 0094.02303 · doi:10.2140/pjm.1960.10.607
[299] Rotman, J., A completion functor on modules and algebras, J. Algebra, 9, 369-387 (1968) · Zbl 0159.05101 · doi:10.1016/0021-8693(68)90009-4
[300] Rotman, J.; Yen, T., Modules over a complete discrete valuation ring, Trans. Am. Math. Soc., 98, 242-254 (1961) · Zbl 0101.02801 · doi:10.1090/S0002-9947-1961-0122895-1
[301] Roux, B., Anneaux non commutatifs de valuation discrète ou finie, scindés, I, C. R. Acad. Sci. Paris. Sér. I. Math., 302, 7, 259-262 (1986) · Zbl 0592.16013
[302] Roux, B., Anneaux non commutatifs de valuation discrète ou finie, scindés, II, C. R. Acad. Sci. Paris. Sér. I. Math., 302, 8, 291-293 (1986) · Zbl 0592.16014
[303] Roux, B., Anneaux non commutatifs de valuation discrète, scindés, en caractéristique zéro, C. R. Acad. Sci. Paris. Sér. I. Math., 303, 14, 663-666 (1986) · Zbl 0608.16007
[304] Roux, B., Hautes σ-dérivations et anneaux de valuation discrète non commutatifs, en caractéristique zéro, C. R. Acad. Sci. Paris. Sér. I. Math., 303, 19, 943-946 (1986) · Zbl 0608.16006
[305] Roux, B., Anneaux de valuation discrète complets, scindés, non commutatifs, en caractéristique zéro, Lect. Notes Math., 1296, 276-311 (1987) · Zbl 0646.16004 · doi:10.1007/BFb0078533
[306] Rowen, LH, Ring Theory (1988), New York: Academic Press, New York · Zbl 0651.16002
[307] Salce, L.; Zanardo, P., Rank-two torsion-free modules over valuation domains, Rend. Sem. Mat. Univ. Padova, 80, 175-201 (1988) · Zbl 0685.13006
[308] A. D. Sands, “On the radical of the endomorphism ring of a primary Abelian group,” in: Abelian Groups and Modules, Springer-Verlag, Vienna (1984), pp. 305-314. · Zbl 0562.20031
[309] Schultz, P., Periodic homomorphism sequences of Abelian groups, Arch. Math., 21, 132-135 (1970) · Zbl 0194.33602 · doi:10.1007/BF01220893
[310] Schultz, P., The endomorphism ring of the additive group of a ring, J. Austr. Math. Soc., 15, 60-69 (1973) · Zbl 0257.20037 · doi:10.1017/S1446788700012763
[311] P. Schultz, “Notes on mixed groups, I,” in: Abelian Groups and Modules, Springer-Verlag, Vienna (1984), pp. 265-278. · Zbl 0566.20039
[312] Schultz, P., Notes on mixed groups, II, Rend. Sem. Mat. Univ. Padova, 75, 67-76 (1986) · Zbl 0588.20032
[313] Schultz, P., When is an Abelian p-group determined by the Jacobson radical of its endomorphism ring?, Contemp. Math., 171, 385-396 (1994) · Zbl 0827.20067 · doi:10.1090/conm/171/01788
[314] P. Schultz, “Automorphisms which determine an Abelian p-group,” in: Abelian Groups, Theory of Modules, and Topology, Marcel Dekker, New York (1998), pp. 373-379. · Zbl 0914.20050
[315] Stefanescu, D., On the factorization of polynomials over discrete valuation domains, An. St. Univ. Ovidius Constanta., 22, 1, 273-280 (2014) · Zbl 1340.11085
[316] Stanton, RO, An invariant for modules over a discrete valuation ring, Proc. Am. Math. Soc., 49, 1, 51-54 (1975) · Zbl 0283.13003 · doi:10.1090/S0002-9939-1975-0360572-8
[317] Stanton, RO, Decomposition bases and Ulm’s theorem, Lect. Notes Math., 616, 39-56 (1977) · Zbl 0374.20063 · doi:10.1007/BFb0068188
[318] Stanton, RO, Relative S-invariants, Proc. Am. Math. Soc., 65, 221-224 (1977) · Zbl 0376.13006
[319] Stanton, RO, Decomposition of modules over a discrete valuation ring, J. Austr. Math. Soc., 27, 284-288 (1979) · Zbl 0427.13008 · doi:10.1017/S1446788700012398
[320] Stanton, RO, Almost affable Abelian groups, J. Pure Appl. Alg., 15, 41-52 (1979) · Zbl 0407.20044 · doi:10.1016/0022-4049(79)90039-2
[321] Stratton, AE, Mixed modules over an incomplete discrete valuation ring, Proc. London Math. Soc., 21, 201-218 (1970) · Zbl 0216.32702 · doi:10.1112/plms/s3-21.2.201
[322] A. E. Stratton, “A note on the splitting problem for modules over an incomplete discrete valuation ring,” Proc. London Math. Soc. (3), 23, 237-250 (1971). · Zbl 0223.13010
[323] Timoshenko, EA, T-radicals and E-radicals in the category of modules, Sib. Mat. Zh., 45, 1, 201-210 (2004) · Zbl 1065.16028 · doi:10.1023/B:SIMJ.0000013022.52517.d8
[324] Timoshenko, EA; Tsarev, AV, Sequences of endomorphism groups of Abelian groups, Mat. Zametki, 104, 2, 309-317 (2018) · Zbl 1398.20065 · doi:10.4213/mzm11711
[325] Tsarev, AV, T-rings and quotient divisible groups of rank 1, Vestn. Tomsk. Univ. Mat. Mekh., 4, 24, 50-53 (2013) · Zbl 07607428
[326] Tuganbaev, AA, Poorly projective modules, Sib. Mat. Zh., 21, 5, 109-113 (1980) · Zbl 0451.16017
[327] Tuganbaev, AA, Serial rings and modules, Mat. Zametki, 48, 2, 99-106 (1990) · Zbl 0756.16001
[328] Tuganbaev, AA, Semidistributive Modules and Rings (1998), Dordrecht-Boston-London: Kluwer Academic, Dordrecht-Boston-London · Zbl 0909.16001 · doi:10.1007/978-94-011-5086-6
[329] Tuganbaev, AA, Distributive Modules and Related Topics (1999), Amsterdam: Gordon and Breach, Amsterdam · Zbl 0962.16003
[330] Tuganbaev, AA, Rings Close to Regular (2002), Dordrecht-Boston-London: Kluwer Academic, Dordrecht-Boston-London · Zbl 1120.16012 · doi:10.1007/978-94-015-9878-1
[331] Ulm, H., Zur Theorie der abzählbar-unendlichen abelschen Gruppen, Math. Ann., 107, 774-803 (1933) · JFM 59.0143.03 · doi:10.1007/BF01448919
[332] R. G. Underwood, “Galois theory of modules over a discrete valuation ring,” in: Recent Research on Pure and Applied Algebra, Nova Sci. Publ., Hauppauge (2003), pp. 23-45. · Zbl 1077.16040
[333] Vámos, P., Decomposition problems for modules over valuation domains, J. London Math. Soc., 41, 10-26 (1990) · Zbl 0736.13013 · doi:10.1112/jlms/s2-41.1.10
[334] R. Vidal, “Anneaux de valuation discrète complets, non nécessairement commutatifs,” C. R. Acad. Sci. Paris. Sér. A-B, 283 (1976). · Zbl 0335.16005
[335] R. Vidal, “Un exemple d’anneax de valuation discrète complet, non commutatif quin’est pas un anneau de Cohen,” C. R. Acad. Sci. Paris. Sér. A-B, 284 (1977). · Zbl 0359.17007
[336] Vidal, R., Anneaux de valuation discrète complets non commutatifs, Trans. Am. Math. Soc., 267, 1, 65-81 (1981) · Zbl 0476.16004
[337] C. Vinsonhaler, “E-rings and related structures,” in: Non-Noetherian commutative ring theory, 520, Math. Apl., Kluwer, Dordrecht (2002), pp. 387-402. · Zbl 0988.16021
[338] Vinsonhaler, C.; Wickless, W., Dualities for torsion-free Abelian groups of finite rank, J. Algebra, 128, 2, 474-487 (1990) · Zbl 0688.20034 · doi:10.1016/0021-8693(90)90035-M
[339] Walker, CL, Local quasi-endomorphism rings of rank one mixed Abelian groups, Lect. Notes Math., 616, 368-378 (1977) · Zbl 0375.20041 · doi:10.1007/BFb0068207
[340] Walker, CL; Warfield, RB Jr, Unique decomposition and isomorphic refinement theorems in additive categories, J. Pure Appl. Algebra, 7, 347-359 (1976) · Zbl 0354.18011 · doi:10.1016/0022-4049(76)90059-1
[341] Walker, EA, Ulm’s theorem for totally projective groups, Proc. Am. Math. Soc., 37, 387-392 (1973) · Zbl 0257.20039
[342] E. A. Walker, “The groups P_β,” in: Symposia Mathematica XIII. Gruppi Abeliani, Academic Press, London (1974), pp. 245-255. · Zbl 0298.20040
[343] Wallace, KD, On mixed groups of torsion free rank one with totally projective primary components, J. Algebra, 17, 482-488 (1971) · Zbl 0215.39902 · doi:10.1016/0021-8693(71)90005-6
[344] Warfied, RB Jr, Homomorphisms and duality for torsion-free groups, Math. Z., 107, 189-200 (1968) · Zbl 0169.03602 · doi:10.1007/BF01110257
[345] Warfied, RB Jr, A Krull-Schmidt theorem for infinite sums of modules, Proc. Am. Math. Soc., 22, 2, 460-465 (1969) · Zbl 0176.31401 · doi:10.1090/S0002-9939-1969-0242886-2
[346] Warfied, RB Jr, Decompositions of injective modules, Pac. J. Math., 31, 263-276 (1969) · Zbl 0185.04102 · doi:10.2140/pjm.1969.31.263
[347] Warfied, RB Jr, An isomorphic refinement theorem for Abelian groups, Pac. J. Math., 34, 1, 237-255 (1970) · Zbl 0206.03401 · doi:10.2140/pjm.1970.34.237
[348] Warfied, RB Jr, Exchange rings and decomposition of modules, Math. Ann., 199, 31-36 (1972) · Zbl 0228.16012 · doi:10.1007/BF01419573
[349] Warfied, RB Jr, Classification theorems for p-groups and modules over a discrete valuation ring, Bull. Am. Math. Soc., 78, 1, 88-92 (1972) · Zbl 0231.13004 · doi:10.1090/S0002-9904-1972-12870-2
[350] R. B. Warfied, Jr., “Simply presented groups,” in: Proc. Special Semester on Abelian Groups, Univ. Arizona, Tucson (1972).
[351] Warfied, RB Jr, A classification theorem for Abelian p-groups, Trans. Am. Math. Soc., 210, 149-168 (1975) · Zbl 0324.20058
[352] Warfied, RB Jr, Classification theory of Abelian groups, I: Balanced projectives, Trans. Am. Math. Soc., 222, 33-63 (1976) · Zbl 0358.20065
[353] Warfied, RB Jr, The structure of mixed Abelian groups, Lect. Notes Math., 616, 1-38 (1977) · Zbl 0368.20032 · doi:10.1007/BFb0068187
[354] Warfied, RB Jr, Cancellation of modules an groups and stable range of endomorphism rings, Pac. J. Math., 91, 2, 457-485 (1980) · Zbl 0484.16017 · doi:10.2140/pjm.1980.91.457
[355] Warfied, RB Jr, Classification theory of Abelian groups, II: Local theory, Lect. Notes Math., 874, 322-349 (1981) · Zbl 0469.20027 · doi:10.1007/BFb0090545
[356] Wick, BD, A projective characterization for SKT-modules, Proc. Am. Math. Soc., 80, 39-43 (1980) · Zbl 0447.20039 · doi:10.1090/S0002-9939-1980-0574505-4
[357] Wick, BD, A classification theorem for SKT-modules, Proc Am. Math. Soc., 80, 44-46 (1980) · Zbl 0447.20040 · doi:10.1090/S0002-9939-1980-0574506-6
[358] Wilson, GV, Modules with the summand intersection property, Commun. Algebra, 14, 1, 21-38 (1986) · Zbl 0592.13008 · doi:10.1080/00927878608823297
[359] Wilson, GV, Additive groups of T-rings, Proc. Am. Math. Soc., 99, 2, 219-220 (1987) · Zbl 0611.20035
[360] Wisbauer, R., Foundations of Module and Ring Theory (1991), Philadelphia: Gordon and Breach, Philadelphia · Zbl 0746.16001
[361] Wolfson, KG, An ideal-theoretic characterization of the ring of all linear transformation, Am. J. Math., 75, 358-386 (1953) · Zbl 0050.11503 · doi:10.2307/2372458
[362] Wolfson, KG, Isomorphisms of the endomorphism rings of torsion-free modules, Proc. Am. Math. Soc., 13, 5, 712-714 (1962) · Zbl 0115.03104 · doi:10.1090/S0002-9939-1962-0142588-0
[363] Wolfson, KG, Isomorphisms of the endomorphism ring of a free module over a principal left ideal domain, Michigan Math. J., 9, 69-75 (1962) · Zbl 0112.02603 · doi:10.1307/mmj/1028998624
[364] Wolfson, KG, Isomorphisms of the endomorphism rings of a class of torsion-free modules, Proc. Am. Math. Soc., 14, 4, 589-594 (1963) · Zbl 0112.02604 · doi:10.1090/S0002-9939-1963-0152551-2
[365] Wolfson, KG, Anti-isomorphisms of endomorphism rings of locally free modules, Math. Z., 202, 151-159 (1989) · Zbl 0655.16016 · doi:10.1007/BF01215251
[366] Yakovlev, AV, On direct decompositions of p-adic groups, Algebra Analiz, 12, 6, 217-223 (2000) · Zbl 1017.16012
[367] Yakovlev, AV, On direct decompositions of S-local groups, Algebra Analiz, 13, 4, 229-253 (2001) · Zbl 1011.20050
[368] Zanardo, P., Kurosch invariants for torsion-free modules over Nagata valuation domains, J. Pure Appl. Algebra, 82, 195-209 (1992) · Zbl 0781.13004 · doi:10.1016/0022-4049(92)90120-5
[369] O. Zariski and P. Samuel, Commutative Algebra, Van Nostrand, Princeton (1958, 1960). · Zbl 0081.26501
[370] J. Žemlička, “Steadiness is tested by a single module,” in: Abelian groups, rings and modules, Perth (2000), pp. 301-308. · Zbl 0988.16003
[371] Zippin, L., Countable torsion groups, Ann. Math., 36, 86-99 (1935) · JFM 61.0104.01 · doi:10.2307/1968666
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.