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On semilocal rings.
- Source :
-
Proceedings of the American Mathematical Society . Sep2008, Vol. 137 Issue 3, p845-852. 8p. - Publication Year :
- 2008
-
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 $R$, $a_0Rsupseteq a_1Rsupseteq a_2Rsupseteq cdots supseteq a_nRsupseteq cdots text { with }a_{i+1}=a_i-a_ib_ia_i$ eventually terminates. Then modules with semilocal endomorphism rings are characterized by chain conditions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 137
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 35290654
- Full Text :
- https://doi.org/10.1090/S0002-9939-08-09577-4