Artinian skew group rings

Park, Jae Keol

doi:10.1090/S0002-9939-1979-0529201-8

Artinian skew group rings
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Proc. Amer. Math. Soc. 75 (1979), 1-7 Request permission

Abstract:

Let R be a ring with identity and let $\theta$ be a group homomorphism from a group G to ${\operatorname {Aut}}(R)$, the group of automorphisms of R. We prove that skew group ring $R{ \ast _\theta }G$ 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.

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