Truman, PJ (2013) Integral Hopf-Galois structures for tame extensions. New York Journal of Mathematics, 19. pp. 647-655. ISSN 1076-9803

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We study the Hopf-Galois module structure of algebraic integers in some Galois extensions of p-adic fields L/K which are at most tamely ramified, generalizing some of the results of the author's 2011 paper cited below. If G=Gal(L/K) and H=L[N]G is a Hopf algebra giving a Hopf-Galois structure on L/K, we give a criterion for the OK-order OL[N]G to be a Hopf order in H. When OL[N]G is Hopf, we show that it coincides with the associated order AH of OL in H and that OL is free over AH, and we give a criterion for a Hopf-Galois structure to exist at integral level. As an illustration of these results, we determine the commutative Hopf-Galois module structure of the algebraic integers in tame Galois extensions of degree qr, where q and r are distinct primes.

Item Type: Article
Uncontrolled Keywords: Hopf-Galois structures; Hopf-Galois module theory; Hopf order; tame ramification
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Depositing User: Symplectic
Date Deposited: 04 Jan 2017 15:17
Last Modified: 24 May 2019 13:10

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