Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
In this note we will determine the associated order of relative extensions of algebraic number fields, which are cyclic of prime order p, assuming that the ground field is linearly disjoint to the pth cyclotomic field, $ℚ^{(p)}$. For quadratic extensions we will furthermore characterize when the ring of integers of the extension field is free over the associated order. All our proofs are quite elementary. As an application, we will determine the Galois module structure of $ℚ^{(n)}/ℚ^{(n)^+}$.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
15-19
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-07-07
Twórcy
autor
- Institut für Mathematik, Karl-Franzens-Universität, Heinrichstr. 36, A-8010 Graz, Österreich
Bibliografia
- [1] Ph. Cassou-Noguès and M. J. Taylor, Elliptic Functions and Rings of Integers, Progr. Math. 66, Birkhäuser, 1987.
- [2] A. Fröhlich, Galois Module Structure of Algebraic Integers, Ergeb. Math. (3) 1, Springer, 1983.
- [3] R. Massy, Bases normales d'entiers relatives quadratiques, J. Number Theory 38 (1991), 216-239.
- [4] W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers, 2nd ed., Springer, 1990.
- [5] K. W. Roggenkamp and M. J. Taylor, Group Rings and Class Groups, DMV Sem. 18, Birkhäuser, 1992.
- [6] M. J. Taylor, Relative Galois module structure of rings of integers, in: Orders and their Applications (Proc. Oberwolfach 1984), I. Reiner and K. W. Roggenkamp (eds.), Lecture Notes in Math. 1142, Springer, 1985, 289-306.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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