Note on the Galois module structure of quadratic extensions

• Autorzy: Günter Lettl
• Języki publikacji: EN

Abstrakty

EN

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 $ℚ^{(n)}/ℚ^{(n)^+}$.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1994
• Tom: 67
• Numer: 1
• Strony: 15-19

Daty

wydano

1994

otrzymano

1993-07-07

Twórcy

autor

Günter Lettl

• 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.