On Hopf DeMeyer-Kanzaki Galois extensions (Q1811935)

Summary: 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 \textit{S. Ikehata} [Math. J. Okayama Univ. 23, 17-18 (1981; Zbl 0475.16003)] is generalized.