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On semilocal rings


Author: Hongbo Zhang
Journal: Proc. Amer. Math. Soc. 137 (2009), 845-852
MSC (2000): Primary 16L30, 16S50, 16P70
DOI: https://doi.org/10.1090/S0002-9939-08-09577-4
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.


References [Enhancements On Off] (What's this?)

  • 1. R. Camps and W. Dicks, On semilocal rings, Israel J. Math. 81, 203-211, 1993. MR 1231187 (94m:16027)
  • 2. A. Facchini, Module Theory: Endomorphism Rings and Direct Sum Decompositions in Some Classes of Modules, Progress in Math., Vol. 167, Birkhäuser Boston, 1998. MR 1634015 (99h:16004)
  • 3. A. Facchini, D. Herbera, L. Levy and P. Vámos, Krull-Schmidt fails for Artinian modules, Proc. Amer. Math. Soc. 123, 3587-3592, 1995. MR 1277109 (96b:16020)
  • 4. D. Herbera and A. Shamsuddin, Modules with semi-local endomorphism ring, Proc. Amer. Math. Soc. 123, 3593-3600, 1995. MR 1277114 (96b:16014)
  • 5. C. Lomp, On dual Goldie dimension, Diplomarbeit, Heinrich Heine Universität, Düsseldorf, 1996.
  • 6. K. Varadarajan, Dual Goldie dimension, Comm. Algebra 7, 565-610, 1979. MR 524269 (80d:16014)

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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: https://doi.org/10.1090/S0002-9939-08-09577-4
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.

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