International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 4, Pages 279-283
Skew group rings which are Galois
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 be a skew group ring of a finite group over a ring . It is shown that if is an -Galois extension of , where is the inner automorphism group of induced by the elements in , then is a -Galois extension
of . A necessary and sufficient condition is also given for the
commutator subring of in to be a Galois extension, where is the subring of the elements fixed
under each element in .