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

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.