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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.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9939-1974-0354788-3
Keywords: Semilocal ring, group of automorphisms, completely outer Galois group, crossed product
Article copyright: © Copyright 1974 American Mathematical Society

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