Commutative Hopf-Galois module structure of tame extensions

Truman

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.

Citation

Truman. (2018). Commutative Hopf-Galois module structure of tame extensions. Journal of Algebra, 389-408. https://doi.org/10.1016/j.jalgebra.2018.01.047

• 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