International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 4, Pages 279-283

Skew group rings which are Galois

George Szeto and Lianyong Xue

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

Received 20 March 1998

Copyright © 2000 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 S*G be a skew group ring of a finite group G over a ring S. It is shown that if S*G is an G-Galois extension of (S*G)G, where G is the inner automorphism group of S*G induced by the elements in G, then S is a G-Galois extension of SG. A necessary and sufficient condition is also given for the commutator subring of (S*G)G in S*G to be a Galois extension, where (S*G)G is the subring of the elements fixed under each element in G.