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.