On prime rings with commuting nilpotent elements
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- by M. Chebotar, P.-H. Lee and E. R. Puczyłowski PDF
- Proc. Amer. Math. Soc. 137 (2009), 2899-2903 Request permission
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.References
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Additional Information
- M. Chebotar
- Affiliation: Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242
- Email: chebotar@math.kent.edu
- P.-H. Lee
- Affiliation: Department of Mathematics, National Taiwan University – and – National Center for Theoretical Sciences, Taipei Office, Taipei, Taiwan
- Email: phlee@math.ntu.edu.tw
- E. R. Puczyłowski
- Affiliation: Institute of Mathematics, University of Warsaw, Banacha 2, Warsaw, Poland
- Email: edmundp@mimuw.edu.pl
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 2899-2903
- MSC (2000): Primary 16N60; Secondary 16N40
- DOI: https://doi.org/10.1090/S0002-9939-09-09894-3
- MathSciNet review: 2506447