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.