International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 1, Pages 37-42
doi:10.1155/S0161171202110386
The Galois algebras and the Azumay Galois extensions
Department of Mathematics, Bradley University, Peoria IL 61625, USA
Received 26 October 2001
Copyright © 2002 George Szeto and Lianyong Xue. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Let B be a Galois algebra over a commutative ring R with Galois group G, C the center of B, K={g∈G|g(c)=c for all c∈C}, Jg{b∈B|bx=g(x)b for all x∈B} for each g∈K, and BK=(⊕∑g∈K Jg). Then BK is a central weakly Galois algebra with Galois group induced by K. Moreover, an Azumaya Galois extension B with Galois group K is characterized by using BK.