Two results on fixed rings

Author:
J.-L. Pascaud

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

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a semiprime ring, a finite group of automorphisms of and the algebra of the group. (A) If is left primitive and is -simple then the fixed subring is left primitive. (B) If is semiprime and is a left Goldie ring, then can be embedded in a free left -module of finite rank. Consequently if is left Noetherian, is left Noetherian.

**[1]**M. Cohen and S. Montgomery,*The normal closure of a semiprime ring*, Ring theory (Proc. Antwerp Conf. (NATO Adv. Study Inst.), Univ. Antwerp, Antwerp, 1978) Lecture Notes in Pure and Appl. Math., vol. 51, Dekker, New York, 1979, pp. 43–59. MR**563284****[2]**Daniel R. Farkas and Robert L. Snider,*Noetherian fixed rings*, Pacific J. Math.**69**(1977), no. 2, 347–353. MR**0444714****[3]**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****[4]**V. K. Kharchenko,*Fixed elements under a finite group acting on a semi-prime ring*, Algebra and Logic**14**(1976), 203-213.**[5]**-,*Galois theory of semi-prime rings*, Algebra and Logic**16**(1978), 208-258.**[6]**Susan Montgomery,*Fixed rings of finite automorphism groups of associative rings*, Lecture Notes in Mathematics, vol. 818, Springer, Berlin, 1980. MR**590245****[7]**Susan Montgomery,*Outer automorphisms of semi-prime rings*, J. London Math. Soc. (2)**18**(1978), no. 2, 209–220. MR**509936**, https://doi.org/10.1112/jlms/s2-18.2.209

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1981-0614870-3

Keywords:
Finite group of automorphisms acting on a ring,
primitive ring,
semiprime Goldie ring

Article copyright:
© Copyright 1981
American Mathematical Society