On a Class of Azumaya Galois Extensions

Abstract

Let B be a ring with 1, G a nite automorphism group of B, C the center of B, K = fg P G j g(c) = c for all c P Cg, and J g = fb P B j bx = g(x)b for all x P Bg for each g P G. Then, B is an Azumaya Galois extension with Galois group G and J g = f0g for each g T P K if and only if B is a commutator Galois extension of B K with Galois group K and B K is a DeMeyer-Kanzaki Galois extension of B G with Galois group G=K. More equivalent conditions are also given in terms of Azumaya skew group rings.