International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 2, Pages 235-238
doi:10.1155/S0161171298000337
Separable subalgebras of a class of Azumaya algebras
Department of Mathematics, Bradley University, Peoria 61625, Illinois, USA
Received 15 July 1996; Revised 14 April 1997
Copyright © 1998 George Szeto. 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.