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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On semilocal rings


Author: Hongbo Zhang
Journal: Proc. Amer. Math. Soc. 137 (2009), 845-852
MSC (2000): Primary 16L30, 16S50, 16P70
Published electronically: September 17, 2008
MathSciNet review: 2457422
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Abstract: In this paper, semilocal rings are characterized in different ways; in particular, it is proved that a ring $ R$ is semilocal if and only if every descending chain of principal right ideals of $ R$, $ a_0R\supseteq a_1R\supseteq a_2R\supseteq \cdots \supseteq a_nR\supseteq \cdots$    with $ a_{i+1}=a_i-a_ib_ia_i$ eventually terminates. Then modules with semilocal endomorphism rings are characterized by chain conditions.


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Additional Information

Hongbo Zhang
Affiliation: School of Physics and Mathematics, Jiangsu Polytechnic University, Changzhou, Jiangsu 213016, People’s Republic of China
Email: hbzhang1212@yahoo.com.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09577-4
PII: S 0002-9939(08)09577-4
Keywords: Semilocal rings, hollow dimension, uniform dimension.
Received by editor(s): December 6, 2007
Received by editor(s) in revised form: March 1, 2008
Published electronically: September 17, 2008
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.