Truman, PJ (2011) Towards a generalisation of Noether's theorem to nonclassical Hopf-Galois structures. New York Journal of Mathematics, 17. pp. 799-810.

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Abstract

We study the nonclassical Hopf-Galois module structure of rings of algebraic integers in some extensions of p-adic fields and number fields which are at most tamely ramified. We show that if L/K is an unramified extension of p-adic fields which is H-Galois for some Hopf algebra H then OL is free over its associated order AH in H. If H is commutative, we show that this conclusion remains valid in ramified extensions of p-adic fields if p does not divide the degree of the extension. By combining these results we prove a generalisation of Noether's theorem to nonclassical Hopf-Galois structures on domestic extensions of number fields.

Item Type: Article
Uncontrolled Keywords: Noether's theorem, Hopf-Galois structures, domestic extensions
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Natural Sciences > School of Computing and Maths
Depositing User: Symplectic
Date Deposited: 04 Jan 2017 15:29
Last Modified: 11 Jun 2019 10:28
URI: http://eprints.keele.ac.uk/id/eprint/2702

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