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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Dinh Van Huynh, S. K. Jain and S. R. López-Permouth
Journal: Proc. Amer. Math. Soc. 128 (2000), 3153-3157
MSC (1991): Primary 16P60, 16N60, 16D80
Published electronically: May 2, 2000
MathSciNet review: 1670375
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] Nguyen Viet Dung, Dinh Van Huynh, Patrick F. Smith, and Robert Wisbauer, Extending modules, Pitman Research Notes in Mathematics Series, vol. 313, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1994. With the collaboration of John Clark and N. Vanaja. MR 1312366 (96f:16008)
  • [2] Carl Faith, Algebra. I. Rings, modules, and categories, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 190, Springer-Verlag, Berlin-New York, 1981. Corrected reprint. MR 623254 (82g:16001)
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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: http://dx.doi.org/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
Published electronically: May 2, 2000
Communicated by: Ken Goodearl
Article copyright: © Copyright 2000 American Mathematical Society