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Commutative Hopf-Galois module structure of tame extensions

Truman

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Abstract

We prove three theorems concerning the Hopf-Galois module structure of fractional ideals in a finite tamely ramified extension of p-adic fields or number fields which is H-Galois for a commutative Hopf algebra H. Firstly, we show that if L/K is a tame Gable extension of p-adic fields then each fractional ideal of L is free over its associated order in H. We also show that this conclusion remains valid if L/K is merely almost classically Galois. Finally, we show that if L/K is an abelian extension of number fields then every ambiguous fractional ideal of L is locally free over its associated order in H. (C) 2018 Elsevier Inc. All rights reserved.

Acceptance Date Feb 14, 2018
Publication Date Jun 1, 2018
Journal Journal of Algebra
Print ISSN 0021-8693
Publisher Elsevier
Pages 389-408
DOI https://doi.org/10.1016/j.jalgebra.2018.01.047
Keywords Hopf-Galois structure, Hopf-Galois module theory, Galois module structure, Associated order
Publisher URL http://dx.doi.org/10.1016/j.jalgebra.2018.01.047

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