Two results on fixed rings
Author:
J.L. Pascaud
Journal:
Proc. Amer. Math. Soc. 82 (1981), 517520
MSC:
Primary 16A74; Secondary 16A20
MathSciNet review:
614870
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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.
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M.
Cohen and S.
Montgomery, The normal closure of a semiprime ring, Ring
theory (Proc. Antwerp Conf. (NATO Adv. Study Inst.), Univ. Antwerp,
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Dekker, New York, 1979, pp. 43–59. MR 563284
(81k:16008)
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Daniel
R. Farkas and Robert
L. Snider, Noetherian fixed rings, Pacific J. Math.
69 (1977), no. 2, 347–353. MR 0444714
(56 #3064)
 [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
(81i:16001)
 [4]
V. K. Kharchenko, Fixed elements under a finite group acting on a semiprime ring, Algebra and Logic 14 (1976), 203213.
 [5]
, Galois theory of semiprime rings, Algebra and Logic 16 (1978), 208258.
 [6]
Susan
Montgomery, Fixed rings of finite automorphism groups of
associative rings, Lecture Notes in Mathematics, vol. 818,
Springer, Berlin, 1980. MR 590245
(81j:16041)
 [7]
Susan
Montgomery, Outer automorphisms of semiprime rings, J. London
Math. Soc. (2) 18 (1978), no. 2, 209–220. MR 509936
(80b:16028), http://dx.doi.org/10.1112/jlms/s218.2.209
 [1]
 M. Cohen and S. Montgomery, The normal closure of a semiprime ring, (Proc. 1978 Antwerp Conf.), Ring Theory, Dekker, New York, 1979, pp. 4359. MR 563284 (81k:16008)
 [2]
 D. Farkas and R. Snider, Noetherian fixed rings, Pacific J. Math. 69 (1977), 347353. MR 0444714 (56:3064)
 [3]
 J. Fisher and J. Osterburg, Finite actions on non commutative rings: a survey since 1970, (Proc. 3rd Oklahoma Conf., 1979), Ring Theory and Algebra III, Dekker, New York, 1980. MR 584618 (81i:16001)
 [4]
 V. K. Kharchenko, Fixed elements under a finite group acting on a semiprime ring, Algebra and Logic 14 (1976), 203213.
 [5]
 , Galois theory of semiprime rings, Algebra and Logic 16 (1978), 208258.
 [6]
 S. Montgomery, Fixed rings of finite automorphism groups of associative rings, Lecture Notes in Math., vol. 818, SpringerVerlag, Berlin and New York. MR 590245 (81j:16041)
 [7]
 , Outer automorphisms of semiprime rings, J. London Math. Soc. 18 (1978), 209221. MR 509936 (80b:16028)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198106148703
PII:
S 00029939(1981)06148703
Keywords:
Finite group of automorphisms acting on a ring,
primitive ring,
semiprime Goldie ring
Article copyright:
© Copyright 1981
American Mathematical Society
