International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 10, Pages 657-662
doi:10.1155/S0161171200003124
The general Ikehata theorem for H-separable crossed products
Department of Mathematics, Bradley University, Peoria 61625, Illinois, USA
Received 26 March 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, C the center of B, G an automorphism group of B of order n for some integer n, CG the set of elements in C fixed under G, Δ=Δ(B,G,f) a crossed product over B where f is a factor
set from G×G to U(CG). It is shown that Δ is an
H-separable extension of B and VΔ(B) is a commutative
subring of Δ if and only if C is a Galois algebra over
CG with Galois group G|C≅G.