关于Weakly r-clean环（英文）  

Weakly r-Clean Rings

作　　者：孟文静[1] 陈焕艮[1] 

机构地区：[1]杭州师范大学理学院,浙江杭州310036

出　　处：《杭州师范大学学报（自然科学版）》2016年第4期394-400,共7页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：Supported by the Natural Science Foundation of Zhejiang Province(LY13A010019)

摘　　要：定义了weakly r-clean环.环R叫做weakly r-clean环,如果对于任意一个元素x∈R可以写成x=r+e或x=r-e的形式,其中r∈Reg(R)且e∈Id(R).首先,证明了在什么情况下weakly r-clean环是weakly clean的.然后,得到了weakly r-clean环的一些性质.进而推广了r-clean环的相应结果.This paper defines weakly r clean rings. A ring R is a weakly r-clean ring if every element xER can be written in the form x=r＋e or x=r--e where rEReg（R） and eC-Id（R）. Firstly, various conditions un- der which a weakly r-clean ring is weakly clean are investigated. Further, some properties of weakly r-elean rings are explored. These extend the corresponding results on r-clean rings.

关 键 词：CLEAN环 正则元 幂等元 r-clean环 WEAKLY r-clean环 

分 类 号：O153.3[理学—数学]