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Nakahara, Toru

On the indices and integral bases of non-cyclic but Abelian biquadratic fields. (English) Zbl 0513.12005

Arch. Math. 41, 504-508 (1983).
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Cited in 2 Reviews
Cited in 22 Documents

MSC:

11R16 Cubic and quartic extensions
11R18 Cyclotomic extensions

Keywords:

Abelian biquadratic field; minimum index; field index; integral basis; power basis

Citations:

Zbl 0016.00803; Zbl 0482.12001
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Full Text: DOI

References:

[1] E. T. Engström, On the common index divisors of an algebraic fields. Trans. Amer. Math. Soc.32, 223-237 (1930). · doi:10.1090/S0002-9947-1930-1501535-0
[2] M. -N.Gras, Z-basis d’entiers 1,?,? 2,? 3 dans les extensions cycliques de degre 4 deQ. Publ. Math. Univ. de Besançon. Theorie des nombres, 1-14 (1980-81).
[3] M. Hall, Indices in cubic fields. Bull. Amer. Math. Soc.43, 104-108 (1937). · Zbl 0016.00803 · doi:10.1090/S0002-9904-1937-06503-7
[4] H. Hasse, Arithmetische Bestimmung von Grundeinheit und Klassenzahl in zyklischen und biquadratischen Zahlkörpern. Abh. Deutsch. Akad. Wiss. Berlin, Math.-Nat. Kl.2, 3-95 (1950) (=Math. Abhandlungen Bd. 3, 289-379 Berlin-New York 1975). · Zbl 0035.30502
[5] H. W. Leopoldt, Über die Hauptordnung der ganzen Elemente eines abelschen Zahlkörpers. J. Reine Angew. Math.201, 119-149 (1958). · Zbl 0098.03403
[6] Y. Motoda, On biquadratic fields. Mem. Fac. Sci. Kyushu Univ. Ser. A29, 263-268 (1975). · Zbl 0314.12012 · doi:10.2206/kyushumfs.29.263
[7] T. Nakahara, On cyclic biquadratic fields related to a problem of Hasse. Monatsh. Math.94, 125-132 (1982). · Zbl 0482.12001 · doi:10.1007/BF01301930
[8] T. Nakahara, On abelian biquadratic fields related to a problem of Hasse. Math. Forschungsinst. Oberwolfach Tagungsb.35/81, 17-18 (1981).
[9] W.Narkiewicz, Elementary and analytic theory of algebraic numbers. Warsaw 1974. · Zbl 0276.12002
[10] E. Von ?yli?ski, Zur Theorie der außerwesentlichen Diskriminantenteiler algebraischer Körper. Math. Ann.73, 273-274 (1913). · JFM 44.0241.02 · doi:10.1007/BF01456716
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