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Proceedings of the American Mathematical Society

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

 
 

 

Completely outer groups of automorphisms acting on $R/J(R)$


Author: J. Osterburg
Journal: Proc. Amer. Math. Soc. 46 (1974), 187-190
MSC: Primary 16A74
DOI: https://doi.org/10.1090/S0002-9939-1974-0354788-3
MathSciNet review: 0354788
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Abstract: Let $R$ be a ring with unit, $J(R)$ its Jacobson radical, and assume $R/J(R)$ Artinian. Let $G$ be a finite group of automorphisms of $R$ that induces a completely outer group on $R/J(R)$. Then $R$ is $G$-Galois over the fixed ring, $S$, if $R$ is projective over the usual crossed product, $\Delta$, or, if the order of $G$ is invertible in $R$, or if $R$ is Artinian.


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Keywords: Semilocal ring, group of automorphisms, completely outer Galois group, crossed product
Article copyright: © Copyright 1974 American Mathematical Society