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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
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?)

  • [1] Yôichi Miyashita, Finite outer Galois theory of non-commutative rings, J. Fac. Sci. Hokkaido Univ. Ser. I 19 (1966), 114–134. MR 0210752
  • [2] Yôichi Miyashita, Galois extensions and crossed products, J. Fac. Sci. Hokkaido Univ. Ser. I 20 (1968), 122–134. MR 0238902
  • [3] Kiiti Morita, Duality for modules and its applications to the theory of rings with minimum condition, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 6 (1958), 83–142. MR 0096700
  • [4] Tadasi Nakayama, Galois theory for general rings with minimum condition, J. Math. Soc. Japan 1 (1949), 203–216. MR 0037283

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DOI: http://dx.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