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

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.