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Commuting Hopf-Galois structures on a separable extension

Truman

Commuting Hopf-Galois structures on a separable extension Thumbnail


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Abstract

Let L/K be a finite separable extension of local or global fields in any characteristic, let H-1, H-2 be two Hopf algebras giving Hopf-Galois structures on the extension, and suppose that the actions of H-1, H-2 on L commute. We show that a fractional ideal B of L is free over its associated order in H-1 if and only if it is free over its associated order in H-2. We also study which properties these associated orders share.

Acceptance Date Jun 3, 2017
Publication Date Feb 1, 2018
Publicly Available Date Mar 28, 2024
Journal Communications in Algebra
Print ISSN 0092-7872
Publisher Taylor and Francis
Pages 1420-1427
DOI https://doi.org/10.1080/00927872.2017.1346107
Keywords mathematics, associated order, Galois module structure, Hopf-Galois module theory, Hopf-Galois structure
Publisher URL http://www.tandfonline.com/doi/full/10.1080/00927872.2017.1346107

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