Separable Subalgebras of a Class of Azumaya Algebras

Let S be a ring with 1, C the center of S, G a finite automorphism group of S of order n invertible in S, and SG the subnng of elements of S fixed under each element in G. It is shown that the skew group ring S,G is a G’-Galois extension of (S,G)G’ that is a projective separable CG-algebra where G’ is the inner automorphism group of S,G induced by G if and only if S is a G-Galois extension of S that is a projective separable CG-algebra. Moreover, properties of the separable subalgebras of a G-Galois H-separable extension S of SG are given when SG is a projective separable CG-algebra.