International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 5, Pages 289-294
doi:10.1155/S0161171200004099
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.
Abstract
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.