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Proceedings of the American Mathematical Society

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On prime rings with commuting nilpotent elements

Authors: M. Chebotar, P.-H. Lee and E. R. Puczyłowski
Journal: Proc. Amer. Math. Soc. 137 (2009), 2899-2903
MSC (2000): Primary 16N60; Secondary 16N40
Published electronically: March 30, 2009
MathSciNet review: 2506447
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Abstract: Let $ R$ be a prime ring in which the nilpotent elements commute. If $ R$ has finite right uniform dimension or its maximal right quotient ring is Dedekind finite, then $ R$ contains no nonzero nilpotent elements.

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Additional Information

M. Chebotar
Affiliation: Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242

P.-H. Lee
Affiliation: Department of Mathematics, National Taiwan University – and – National Center for Theoretical Sciences, Taipei Office, Taipei, Taiwan

E. R. Puczyłowski
Affiliation: Institute of Mathematics, University of Warsaw, Banacha 2, Warsaw, Poland

Keywords: Prime ring, maximal right quotient ring, nilpotent element
Received by editor(s): December 8, 2008
Published electronically: March 30, 2009
Additional Notes: The third author was supported in part by MNiSW Grant Nr N N201 268435
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.