International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 5, Pages 289-294
On central commutator Galois extensions of rings
Mathematics Department, Bradley University, Peoria 61625, Illinois, USA
Received 17 November 1999
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 ring with , a finite automorphism group of of order for some integer ,
the set of elements in fixed under each element in , and
commutator subring of in . Then the type of central
commutator Galois extensions is studied. This type includes the
types of Azumaya Galois extensions and Galois -separable
extensions. Several characterizations of a central commutator
Galois extension are given. Moreover, it is shown that when is
inner, is a central commutator Galois extension of if and
only if is an -separable projective group ring .
This generalizes the structure theorem for central Galois algebras
with an inner Galois group proved by DeMeyer.