International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 5, Pages 289-294

On central commutator Galois extensions of rings

George Szeto and Lianyong Xue

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 B be a ring with 1, G a finite automorphism group of B of order n for some integer n, BG the set of elements in B fixed under each element in G, and Δ=VB(BG) the commutator subring of BG in B. Then the type of central commutator Galois extensions is studied. This type includes the types of Azumaya Galois extensions and Galois H-separable extensions. Several characterizations of a central commutator Galois extension are given. Moreover, it is shown that when G is inner, B is a central commutator Galois extension of BG if and only if B is an H-separable projective group ring BGGf. This generalizes the structure theorem for central Galois algebras with an inner Galois group proved by DeMeyer.