Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

On the symmetry of the Goldie and CS conditions for prime rings

Author(s): Dinh Van Huynh; S. K. Jain; S. R. López-Permouth
Journal: Proc. Amer. Math. Soc. 128 (2000), 3153-3157.
MSC (1991): Primary 16P60, 16N60, 16D80
Posted: May 2, 2000
MathSciNet review: 1670375
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Abstract | References | Similar articles | Additional information

Abstract: It is shown that: (a) If is a prime right Goldie right CS ring with right uniform dimension at least 2, then is left Goldie, left CS; (b) A semiprime ring is right Goldie left CS iff is left Goldie, right CS.

References:

[1]: N.V. Dung, D.V. Huynh, P.F. Smith and R. Wisbauer, Extending Modules, Research Notices in Mathematics Series 313, Pitman, London (1994). MR 96f:16008
[2]: C. Faith, Algebra I: Rings Modules, and Categories of Modules, Springer-Verlag, Berlin-Heidelberg-New York 1981. MR 82g:16001
[3]: K.R. Goodearl, Ring Theory: Nonsingular Rings and Modules, Marcel Dekker, New York-Basel 1968. MR 55:2970
[4]: I.N. Herstein, Noncommutative Rings, The Carus Mathematical Monograph No 15, Math. Ass. Amer. 1973. MR 37:2790

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