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International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 10, Pages 657-662
http://dx.doi.org/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 Hindawi Publishing Corporation. 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|CG.