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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Artinian skew group rings


Author: Jae Keol Park
Journal: Proc. Amer. Math. Soc. 75 (1979), 1-7
MSC: Primary 16A26
DOI: https://doi.org/10.1090/S0002-9939-1979-0529201-8
MathSciNet review: 529201
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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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DOI: https://doi.org/10.1090/S0002-9939-1979-0529201-8
Keywords: Skew group rings, semilocal rings, perfect rings, semiperfect rings, semiprimary rings, crossed products, outer automorphism
Article copyright: © Copyright 1979 American Mathematical Society