Some Results on Semilocal Rings

被引：0
|
作者：
Zhang, Hongbo [1 ]
机构：
[1] Changzhou Univ, Sch Math & Phys, Changzhou, Jiangsu 213016, Peoples R China
来源：
VIETNAM JOURNAL OF MATHEMATICS | 2015年 / 43卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Semilocal ring; Endomorphism ring; Semisimple module;
D O I：
10.1007/s10013-014-0095-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We first give simple proofs to some main results on semilocal rings of Zhang (Proc. Amer. Math. Soc. 137, 845-852, 2009). Then, as an extension, we prove that the R/J (R)-module (aR) over bar is semisimple if and only if every descending chain in aR : a(1) R. superset of center dot center dot center dot superset of a(n)R superset of center dot center dot center dot with a(i)+1 = a(i) - a(i)b(i)a(i) (i = 1, 2,...) eventually terminates.
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页码：551 / 556
页数：6
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