Found 108 Documents (Results 1–100)
On monogenity of certain pure number fields of degrees \(2^r\cdot 3^k\cdot 7^s\). (English) Zbl 07893417
On common index divisors and monogenity of septic number fields defined by trinomials of type \(x^7 + ax^2 + b\). (English) Zbl 07857904
Reviewer: István Gaál (Debrecen)
Calculating generators of power integral bases in pure sextic fields. (English) Zbl 07836768
Reviewer: Dimitros Poulakis (Thessaloniki)
On index divisors and monogenity of certain number fields defined by \(x^{12}+ax^m+b\). (English) Zbl 07796584
On the index divisors and monogenity of number fields defined by \(x^5 + ax^3 + b\). (English) Zbl 07755241
Reviewer: Toufik Zaïmi (Riyadh)
On the index of the octic number field defined by \(x^8 + ax + b\). (English) Zbl 1538.11178
Reviewer: István Gaál (Debrecen)
On nonmonogenic number fields defined by trinomials of type \(x^n +ax^m+b\). (English) Zbl 1532.11148
Reviewer: Masanari Kida (Tōkyō)
Monogenity in totally real extensions of imaginary quadratic fields with an application to simplest quartic fields. (English) Zbl 07722750
On index divisors and non-monogenity of certain quintic number fields defined by \(x^5 + ax^m + bx + c\). (English) Zbl 1531.11103
Reviewer: Władysław Narkiewicz (Wrocław)
On index divisors and monogenity of certain septic number fields defined by \(x^7 + ax^3 + b\). (English) Zbl 1522.11108
Reviewer: Sudesh Kaur Khanduja (S.A.S. Nagar)
Integral bases and monogenity of pure number fields with non-square free parameters up to degree 9. (English) Zbl 1516.11101
Reviewer: Władysław Narkiewicz (Wrocław)
On monogenity of certain pure number fields defined by \(x^{2^u\cdot 3^v} - m\). (English) Zbl 1538.11180
Reviewer: István Gaál (Debrecen)
On power integral bases of certain pure number fields defined by \(x^{3^r} - m\). (English) Zbl 1512.11076
Reviewer: Władysław Narkiewicz (Wrocław)
On the monogenity of certain binomial compositions. (English) Zbl 1529.11107
Reviewer: Leonard Jones (Shippensburg)
Frobenius finds non-monogenic division fields of abelian varieties. (English) Zbl 1527.11048
Reviewer: Sungkon Chang (Savannah)
Monogenic fields arising from trinomials. (English) Zbl 1515.11105
Reviewer: Sudesh Kaur Khanduja (S.A.S. Nagar)
On monogenity of certain number fields defined by \(x^8+ax+b\). (English) Zbl 1513.11177
Reviewer: István Gaál (Debrecen)
On power integral bases for certain pure number fields. (English) Zbl 1499.11316
Reviewer: István Gaál (Debrecen)
On power integral bases for certain pure number fields defined by \(x^{2\cdot 3^k}-m\). (English) Zbl 1491.11098
Reviewer: Toufik Zaïmi (Riyadh)
On power integral bases of certain pure number fields defined by \(x^{42}-m\). (English) Zbl 1478.11124
On power integral bases for certain pure number fields defined by \(x^{36}-m\). (English) Zbl 1488.11162
Reviewer: István Gaál (Debrecen)
On monogenity of certain pure number fields defined by \(x^{p^r}-m\). (English) Zbl 1483.11236
Reviewer: Artūras Dubickas (Vilnius)
On power integral bases for certain pure number fields defined by \(x^{2^r.5^s}-m\). (English) Zbl 1471.11260
The characterization of cyclic cubic fields with power integral bases. (English) Zbl 1478.11126
Reviewer: Toufik Zaïmi (Riyadh)
On integral bases and monogeneity of pure sextic number fields with non-squarefree coefficients. (English) Zbl 1479.11182
Reviewer: Radoslav M. Dimitrić (New York)
Non-monogenic division fields of elliptic curves. (English) Zbl 1473.11124
Reviewer: Noburo Ishii (Kyoto)
The monogeneity of radical extensions. (English) Zbl 1469.11413
Reviewer: Władysław Narkiewicz (Wrocław)
Integral basis and power integral basis of cubic field. (Chinese. English summary) Zbl 1474.11183
On power integral bases for certain pure number fields defined by \(x^{24}-m\). (English) Zbl 1474.11182
Reviewer: István Gaál (Debrecen)
Calculating relative power integral bases in totally complex quartic extensions of totally real fields. (English) Zbl 1490.11121
Diophantine equations and power integral bases. Theory and algorithms. 2nd edition. (English) Zbl 1465.11090
Cham: Birkhäuser (ISBN 978-3-030-23864-3/hbk; 978-3-030-23867-4/pbk; 978-3-030-23865-0/ebook). xxii, 326 p. (2019).
Reviewer: Andrej Dujella (Zagreb)
On a family of biquadratic fields that do not admit a unit power integral basis. (English) Zbl 1438.11137
Integral bases and monogenity of the simplest sextic fields. (English) Zbl 1409.11085
Reviewer: Władysław Narkiewicz (Wrocław)
Computing relative power integral bases in a family of quartic extensions of imaginary quadratic fields. (English) Zbl 1399.11097
Reviewer: István Gaál (Debrecen)
Integer-valued polynomials on algebras: a survey of recent results and open questions. (English) Zbl 1390.13063
Fontana, Marco (ed.) et al., Rings, polynomials, and modules. Proceedings of the conferences “Recent advances in commutative ring and module theory”, Bressanone/Brixen, Italy, June 13–17, 2016 and “Conference on rings and polynomials”, Graz, Austria, July 3–8, 2016. Cham: Springer (ISBN 978-3-319-65872-8/hbk; 978-3-319-65874-2/ebook). 353-375 (2017).
Reviewer: Władysław Narkiewicz (Wrocław)
Determining elements of minimal index in an infinite family of totally real bicyclic biquadratic number fields. (English) Zbl 1373.11077
Non-monogenity in a family of octic fields. (English) Zbl 1381.11102
Reviewer: Artūras Dubickas (Vilnius)
Calculating power integral bases by using relative power integral bases. (English) Zbl 1395.11121
Reviewer: Władysław Narkiewicz (Wrocław)
Approximation of eigenfunctions in kernel-based spaces. (English) Zbl 1353.65139
Reviewer: Seenith Sivasundaram (Daytona Beach)
A hybrid Gröbner bases approach to computing power integral bases. (English) Zbl 1374.11085
Reviewer: Michael Pohst (Düsseldorf)
Power integral bases in a family of sextic fields with quadratic subfields. (English) Zbl 1393.11068
MSC:
11R04
Sextic extension with cubic subfield. (English) Zbl 1307.11112
MSC:
11R16
Application of Weierstrass units to relative power integral bases. (English) Zbl 1326.11063
Reviewer: Péter Olajos (Miskolc)
Power integral bases for certain pure sextic fields. (English) Zbl 1316.11094
Reviewer: James E. Carter (Charleston)
Relative power integral bases in infinite families of quartic extensions of quadratic fields. (English) Zbl 1335.11094
Self-dual integral normal bases and Galois module structure. (English) Zbl 1292.11128
Reviewer: Bouchaïb Sodaïgui (Valenciennes)
On power bases for rings of integers of relative Galois extensions. (English) Zbl 1318.11135
Reviewer: István Gaál (Debrecen)
\(\mathrm{PSL}(2,7)\) septimic fields with a power basis. (English. French summary) Zbl 1280.11062
Reviewer: István Gaál (Debrecen)
On existence of canonical number system in certain classes of pure algebraic number fields. (English) Zbl 1268.11147
Reviewer: István Gaál (Debrecen)
On biquadratic fields that admit unit power integral basis. (English) Zbl 1265.11097
Reviewer: Péter Olajos (Miskolc)
On the rates of convergence of Bernstein-Chlodovsky polynomials and their Bézier-type variants. (English) Zbl 1217.41018
Reviewer: Martin D. Buhmann (Gießen)
Monogeneity in cyclotomic fields. (English) Zbl 1211.11117
Reviewer: István Gaál (Debrecen)
Power bases for rings of integers of abelian imaginary fields. (English) Zbl 1227.11108
Reviewer: István Gaál (Debrecen)
On the rates of convergence of Chlodovsky-Durrmeyer operators and their Bézier variant. (English) Zbl 1181.41028
Hasse’s problem for monogenic fields. (English) Zbl 1187.11038
Reviewer: István Gaál (Debrecen)
MSC:
11R04
Root bases of polynomials over integral domains. (English) Zbl 1185.13025
Göbel, Rüdiger (ed.) et al., Models, modules and Abelian groups. In memory of A. L. S. Corner. Berlin: Walter de Gruyter (ISBN 978-3-11-019437-1/hbk). 235-248 (2008).
Reviewer: Jebrel M. Habeb (Irbid)
Monogenic \(A_4\) quartic fields. (English) Zbl 1190.11057
Reviewer: István Gaál (Debrecen)
Power bases for the cyclotomic field \(\mathbb Q(\zeta_{15})\). (English) Zbl 1127.11074
Reviewer: Zhang Xianke (Beijing)
Power integral bases in the family of simplest quartic fields. (English) Zbl 1092.11042
Reviewer: Władysław Narkiewicz (Wrocław)
Recent progress of Hasse’s problem on power integral bases of abelian fields. (English) Zbl 1064.11068
Kim, H. K. (ed.) et al., Proceedings of the Japan-Korea joint seminar on number theory, October 9–12, 2004, Kuju, Japan. Fukuoka: Kyushu University. 131-136 (2004).
Reviewer: Artūras Dubickas (Vilnius)
MSC:
11R04
\(p\)-integral bases of a quartic field defined by a trinomial \(x^4+ax+b\). (English) Zbl 1050.11091
Reviewer: Władysław Narkiewicz (Wrocław)
On a theorem of Childs on normal bases of rings of integers: Addendum. (English) Zbl 1083.11070
Reviewer: Lindsay N. Childs (Albany)
MSC:
11R33
On power basis in cyclic fields the conductur of which is a power of Mersenne prime. (English) Zbl 1065.11085
Reviewer: Władysław Narkiewicz (Wrocław)
Note on the ring of integers of a Kummer extension of prime degree. I. (English) Zbl 1058.11063
Reviewer: Lindsay N. Childs (Albany)
On a theorem of Childs on normal bases of rings of integers. (English) Zbl 1048.11087
Reviewer: Lindsay N. Childs (Albany)
A prototype of certain abelian fields whose rings of integers have a power basis. (English) Zbl 1061.11057
Reviewer: Franz Lemmermeyer (Bilkent)
Diophantine equations and power integral bases. New computational methods. (English) Zbl 1016.11059
Boston, MA: Birkhäuser. xviii, 184 p. (2002).
Reviewer: Michael Pohst (Berlin)
Computing all monogeneous mixed dihedral quartic extensions of a quadratic field. (English) Zbl 1065.11086
Reviewer: Nikos Tzanakis (Iraklion)
A note on integral bases of unramified cyclic extensions of prime degree. II. (English) Zbl 0991.11058
Reviewer: Cornelius Greither (Neubiberg)
A note on integral bases of unramified cyclic extensions of prime degree. (English) Zbl 1018.11055
Reviewer: Lindsay N.Childs (Albany)
On a power integral bases problem over cyclotomic \(\mathbb{Z}_p\)-extensions. (English) Zbl 0990.11060
Reviewer: Franz Lemmermeyer (San Marcos)
Power integral bases in composites of number fields. (English) Zbl 0951.11012
Reviewer: Nikos Tzanakis (Iraklion)
Canonical number systems and automata. (Kanonische Ziffersysteme und Automaten.) (German) Zbl 0905.11009
Reviewer: A.Pethő (Debrecen)
Power integral bases in a parametric family of totally real cyclic quintics. (English) Zbl 0899.11064
Reviewer: N.Tzanakis (Iraklion)
On the resolution of index form equations in sextic fields with an imaginary quadratic subfield. (English) Zbl 0873.11025
Reviewer: N.Tzanakis (Iraklion)
Determining the monogeneity of a quartic number field. (English) Zbl 0839.11048
Reviewer: M.Pohst (Berlin)
Generalized Fourier expansions for zero-solutions of surjective convolution operators on \({\mathcal D}_\{\omega\}({\mathbb{R}})'\). (English) Zbl 0674.46021
Reviewer: R.Meise
Computing all power integral bases of cubic fields. (English) Zbl 0677.10013
Reviewer: J.H.Evertse
Construction of power integral bases in ray class fields over imaginary-quadratic number fields. (Konstruktion von Potenzganzheitsbasen in Strahlklassenkörpern über imaginär-quadratischen Zahlkörpern.) (German) Zbl 0666.12006
Reviewer: Reinhard Schertz
A note on normal and power bases. (English) Zbl 0632.12010
Reviewer: R.Massy
Elliptic functions and the generation of rings of integers. (Fonctions elliptiques et génération d’anneaux d’entiers.) (French) Zbl 0621.12012
Journées arithmétiques, Besançon/France 1985, Astérisque 147-148, 49-70 (1987).
Reviewer: Jean Cougnard
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