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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
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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