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International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 12, Pages 753-758
http://dx.doi.org/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 Hindawi Publishing Corporation. 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=gGJg where Jg={bB|bx=g(x)bfor allxB}, then there exist orthogonal central idempotents {fiC|i=1,2,,mfor some integerm} and subgroups Hi of G such that B=(i=1mBfi)D where Bfi is a central Galois algebra with Galois group Hi|BfiHi for each i=1,2,,m and D is contained in C.