International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 12, Pages 753-758
doi:10.1155/S0161171201006068
On Azumaya algebras with a finite automorphism group
Department of Mathematics, Bradley University, Peoria 61625, IL, USA
Received 26 October 2000
Copyright © 2001 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 ring with 1, C the center of B, and G a finite automorphism group of B. It is shown that if B is an Azumaya algebra such that B=⊕∑g∈GJg where Jg={b∈B|bx=g(x)b for all x∈B}, then there exist orthogonal central idempotents {fi∈C|i=1,2,…,m for some integer m} and subgroups Hi of G such that B=(⊕∑i=1mBfi)⊕D where Bfi is a central Galois algebra with Galois group Hi|Bfi≅Hi for each i=1,2,…,m and D is contained in C.