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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Two results on fixed rings


Author: J.-L. Pascaud
Journal: Proc. Amer. Math. Soc. 82 (1981), 517-520
MSC: Primary 16A74; Secondary 16A20
MathSciNet review: 614870
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Abstract: Let $ R$ be a semiprime ring, $ G$ a finite group of automorphisms of $ R$ and $ B$ the algebra of the group. (A) If $ R$ is left primitive and $ B$ is $ G$-simple then the fixed subring $ {R^G}$ is left primitive. (B) If $ B$ is semiprime and $ {R^G}$ is a left Goldie ring, then $ R$ can be embedded in a free left $ {R^G}$-module of finite rank. Consequently if $ {R^G}$ is left Noetherian, $ R $ is left Noetherian.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0614870-3
PII: S 0002-9939(1981)0614870-3
Keywords: Finite group of automorphisms acting on a ring, primitive ring, semiprime Goldie ring
Article copyright: © Copyright 1981 American Mathematical Society