Skew group rings which are Galois

Abstract

Let S*G be a skew group ring of a finite group G over a ring S. It is shown that if S*G is an G′-Galois extension of (S*G)G′, where G′ is the inner automorphism group of S*G induced by the elements in G, then S is a G-Galois extension of SG. A necessary and sufficient condition is also given for the commutator subring of (S*G)G′ in S*G to be a Galois extension, where (S*G)G′ is the subring of the elements fixed under each element in G′.

Keywords

• Skew group rings
• Azumaya algebras
• Galois extensions
• H-separable extensions.