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

Dinh Van Huynh
Affiliation: Institute of Mathematics, P.O. Box 631 Boho, Hanoi, Vietnam - Department of Mathematics, Ohio University, Athens, Ohio 45701

S. K. Jain
Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701

S. R. López-Permouth
Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701

DOI: 10.1090/S0002-9939-00-05381-8
PII: S 0002-9939(00)05381-8
Received by editor(s): May 12, 1998
Received by editor(s) in revised form: September 28, 1998 and December 9, 1998
Posted: May 2, 2000
Communicated by: Ken Goodearl
Copyright of article: Copyright 2000, American Mathematical Society

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