Two results on fixed rings

Pascaud, J.-L.

doi:10.1090/S0002-9939-1981-0614870-3

Two results on fixed rings
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by J.-L. Pascaud PDF

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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Daniel R. Farkas and Robert L. Snider, Noetherian fixed rings, Pacific J. Math. 69 (1977), no. 2, 347–353. MR 444714
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

Fixed elements under a finite group acting on a semi-prime ring

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Galois theory of semi-prime rings

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Susan Montgomery, Fixed rings of finite automorphism groups of associative rings, Lecture Notes in Mathematics, vol. 818, Springer, Berlin, 1980. MR 590245
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