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
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