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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 26, Pages 1627-1632
http://dx.doi.org/10.1155/S0161171203210565

On Hopf DeMeyer-Kanzaki Galois extensions

Department of Mathematics, Bradley University, Peoria, IL 61625, USA

Received 15 October 2002

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let H be a finite-dimensional Hopf algebra over a field k, B a left H-module algebra, and H the dual Hopf algebra of H. For an H-Azumaya Galois extension B with center C, it is shown that B is an H-DeMeyer-Kanzaki Galois extension if and only if C is a maximal commutative separable subalgebra of the smash product B#H. Moreover, the characterization of a commutative Galois algebra as given by S. Ikehata (1981) is generalized.