A note on completeness and strongly clean rings

被引：2
|
作者：
Diesl, Alexander J. [1 ]
Dorsey, Thomas J. [2 ]
Garg, Shelly [3 ]
Khurana, Dinesh [4 ]
机构：
[1] Wellesley Coll, Dept Math, Wellesley, MA 02481 USA
[2] Ctr Commun Res, San Diego, CA 92121 USA
[3] Indian Inst Sci Educ & Res, Dept Math, Mohali 140306, India
[4] Panjab Univ, Dept Math, Chandigarh 160014, India
来源：
JOURNAL OF PURE AND APPLIED ALGEBRA | 2014年 / 218卷 / 04期
关键词：
TRIANGULAR-MATRIX RINGS; LOCAL-RINGS;
D O I：
10.1016/j.jpaa.2013.08.006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Many authors have investigated the behavior of strong cleanness under certain ring extensions. In this note, we investigate the classical problem of lifting idempotents, in order to consolidate and extend these results. Our main result is that if R is a ring which is complete with respect to an ideal I and if x is an element of R whose image in R/I is strongly pi-regular, then x is strongly clean in R. This generalizes Theorem 2.1 of Chen and Zhou (2007) [9]. (C) 2013 Published by Elsevier B.V.
引用
收藏
页码：661 / 665
页数：5
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