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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the symmetry of the Goldie and CS conditions for prime rings
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by Dinh Van Huynh, S. K. Jain and S. R. López-Permouth PDF
Proc. Amer. Math. Soc. 128 (2000), 3153-3157 Request permission

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
  • 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
  • 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
  • K. R. Goodearl, Ring theory, Pure and Applied Mathematics, No. 33, Marcel Dekker, Inc., New York-Basel, 1976. Nonsingular rings and modules. MR 0429962
  • I. N. Herstein, Noncommutative rings, The Carus Mathematical Monographs, No. 15, Mathematical Association of America; distributed by John Wiley & Sons, Inc., New York, 1968. MR 0227205
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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
  • MR Author ID: 199020
  • S. R. López-Permouth
  • Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701
  • 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
  • © Copyright 2000 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 128 (2000), 3153-3157
  • MSC (1991): Primary 16P60, 16N60, 16D80
  • DOI: https://doi.org/10.1090/S0002-9939-00-05381-8
  • MathSciNet review: 1670375