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On prime rings with commuting nilpotent elements
Author(s):
M.
Chebotar;
P.-H.
Lee;
E.
R.
Puczyłowski
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2899-2903.
MSC (2000):
Primary 16N60;
Secondary 16N40
Posted:
March 30, 2009
MathSciNet review:
2506447
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Abstract |
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Additional information
Abstract:
Let  be a prime ring in which the nilpotent elements commute. If  has finite right uniform dimension or its maximal right quotient ring is Dedekind finite, then  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
DOI:
10.1090/S0002-9939-09-09894-3
PII:
S 0002-9939(09)09894-3
Keywords:
Prime ring,
maximal right quotient ring,
nilpotent element
Received by editor(s):
December 8, 2008
Posted:
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 of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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