The Trace map and Azumaya Galois Extension

摘要

Let S be a ring with 1, G a finite automorphism group of S of order n for some integer n invertible in S, C the center of S, S~G the subring of the elemnts fixed under each element in G, and S * G the skew group ring of G over S. Then S is an Azumaya G-Galois extension of S~G if and only if S * G is an H-separable extension of C an dS is a separable C~G-algebra. Properties of S * G Are given when Tr_G'(g) = 0 for each g not in the center of G where Tr_G' is the Trace of G' and G' is the inner automorphism group of S * G induced by the Elements in G.