杭州师范大学学报（自然科学版）Issue(4)：418-422,5.DOI:10.3969/j.issn.1674-232X.2015.04.015
关于Weakly Almost Clean环
摘要
Abstract
This paper defines weakly almost clean rings .A commutative ring R is a weakly almost clean ring if every element x∈ R can be written in the form x= r+ e or x= r-e where r∈ reg(R) and e∈ Id(R) .Firstly , for a nonempty collection {Ri}of rings Ri ,the product R = ∏ i∈ IRi is weakly almost clean if and only if there exists m∈ I such that Rm is weakly almost clean and Rn is almost clean for all n≠ m .Further ,let R be a ring and M be an R‐module ,the trivial extension R(M) of R and M is weakly almost clean if and only if each x∈ R can be written in the form x= r+ e or x= r-e where r∈ R-(Z(R)∪ Z(M)) and e∈ Id(R) .These extend the corre‐sponding results on almost clean rings .关键词
clean环/零因子/正则元/幂等元/almost clean环Key words
clean ring/zero divisor/regular element/idempotent/almost clean ring分类
数理科学引用本文复制引用
孟文静,陈焕艮..关于Weakly Almost Clean环[J].杭州师范大学学报（自然科学版）,2015,(4):418-422,5.基金项目
Supported by the Natural Science Foundation of Zhejiang Province （LY13A010019）． （）
