Commuting Hopf-Galois structures on a separable extension

Truman

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.

Citation

Truman. (2018). Commuting Hopf-Galois structures on a separable extension. Communications in Algebra, 1420-1427. https://doi.org/10.1080/00927872.2017.1346107

• 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