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International Journal of Mathematics and Mathematical Sciences
Volume 21, Issue 2, Pages 235-238
http://dx.doi.org/10.1155/S0161171298000337

Separable subalgebras of a class of Azumaya algebras

George Szeto

Department of Mathematics, Bradley University, Peoria 61625, Illinois, USA

Received 15 July 1996; Revised 14 April 1997

Copyright © 1998 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 S be a ring with 1, C the center of S, G a finite automorphism group of S of order n invertible in S, and SG the subnng of elements of S fixed under each element in G. It is shown that the skew group ring S*G is a G′-Galois extension of (S*G)G′ that is a projective separable CG-algebra where G′ is the inner automorphism group of S*G induced by G if and only if S is a G-Galois extension of SG that is a projective separable CG-algebra. Moreover, properties of the separable subalgebras of a G-Galois H-separable extension S of SG are given when SG is a projective separable CG-algebra.