强J^(1/2)-clean环  

On Strongly J^(1/2)-clean Rings

作　　者：董李青 

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）》2015年第3期323-328,共6页Journal of Hangzhou Normal University(Natural Science Edition)

摘　　要：定义了环R的一个子集,记做J(R)(12)={a∈R|a2∈J(R)}.称环R中的一个元素a是强J12-clean元,如果存在一个幂等元e∈R和一个元素w∈J(R)(1/2)使得a=e+w且ew=we.如果环R中每个元素都是强J12-clean元,称环R是强J12-clean环.文章研究了强J12-clean环的一些性质和局部环上矩阵环的强J12-clean性.A subset of R is defined and marked as J（R）={a∈ R｜a2 ∈ J（R）} .An element a∈ R is called strongly J12‐clean element ,provided that there exists an idempotent e∈ R and an element w∈ J（R） such that a= e＋ w and ew= we .A ring R is strongly J12‐clean ring if every element in R is strongly J12‐clean element .This article studies the properties of strongly J12‐clean ring and the property of strongly J12‐clean of matrix rings on local rings .

关 键 词：强 J 12-clean环 强 J-clean环 矩阵环 

分 类 号：O153.3[理学—数学]