Artinian skew group rings

Abstract

Let R be a ring with identity and let θ \theta be a group homomorphism from a group G to Aut ( R ) {\operatorname {Aut}}(R) , the group of automorphisms of R. We prove that skew group ring R ∗ θ G R{ \ast _\theta }G is right Artinian (resp., semiprimary, right perfect) if and only if R is right Artinian (resp., semiprimary, right perfect) and the group G is finite. Also semilocal skew group rings over fields are characterized.