International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 1, Pages 37-42

The Galois algebras and the Azumay Galois extensions

George Szeto and Lianyong Xue

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.


Let B be a Galois algebra over a commutative ring R with Galois group G, C the center of B, K={gG|g(c)=cfor all cC}, Jg{bB|bx=g(x)bfor allxB} for each gK, and BK=(gKJg). 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.