Galois Module Structure of Ambiguous Ideals in Biquadratic Extensions

Author:

Elder G. Griffith

Abstract

AbstractLet N/K be a biquadratic extension of algebraic number fields, and G = Gal(N/K). Under a weak restriction on the ramification filtration associated with each prime of K above 2, we explicitly describe the ℤ[G]-module structure of each ambiguous ideal of N. We find under this restriction that in the representation of each ambiguous ideal as a ℤ[G]-module, the exponent (or multiplicity) of each indecomposable module is determined by the invariants of ramification, alone.For a given group, G, define SG to be the set of indecomposable ℤ[G]-modules, M, such that there is an extension, N/K, for which GGal(N/K), and M is a ℤ[G]-module summand of an ambiguous ideal of N. Can SG ever be infinite? In this paper we answer this question of Chinburg in the affirmative.

Publisher

Canadian Mathematical Society

Subject

General Mathematics

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Biquadratic Extensions with One Break;Canadian Mathematical Bulletin;2002-06-01

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