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 2 G j g(c) = c for all c 2 Cg, and Jg = fb 2 B j bx = g(x)b for all x 2 Bg for each g 2 G. Then, B is an Azumaya Galois extension with Galois group G and Jg = f0g for each g 62 K if and only if B is a commutator Galois extension of B with Galois group K and B is a DeMeyer-Kanzaki Galois extension of B with Galois group G=K. More equivalent conditions are also given in terms of Azumaya skew group rings. 2000 Mathematics Subject Classi cation: 16S35, 16W20