Two results on fixed rings
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- Proc. Amer. Math. Soc. 82 (1981), 517-520 Request permission
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.References
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- Joe W. Fisher and James Osterburg, Finite group actions on noncommutative rings: a survey since 1970, Ring theory and algebra, III (Proc. Third Conf., Univ. Oklahoma, Norman, Okla., 1979) Lecture Notes in Pure and Appl. Math., vol. 55, Dekker, New York, 1980, pp. 357–393. MR 584618 V. K. Kharchenko, Fixed elements under a finite group acting on a semi-prime ring, Algebra and Logic 14 (1976), 203-213. —, Galois theory of semi-prime rings, Algebra and Logic 16 (1978), 208-258.
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 82 (1981), 517-520
- MSC: Primary 16A74; Secondary 16A20
- DOI: https://doi.org/10.1090/S0002-9939-1981-0614870-3
- MathSciNet review: 614870