关于Weakly UJ~#环(英)  

On Weakly UJ~# Rings

作　　者：郝亚璞 何亚茹 陈焕艮[1] HAO Yapu;HE Yaru;CHEN Huanyin(School of Science, Hangzhou Normal University, Hangzhou 310036, China)

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）》2018年第1期90-94,共5页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：Supported by the Natural Science Foundation of Zhejiang Province(LY17A010018)

摘　　要：引进了一类新环:环R是弱UJ~#环,如果所有的可逆元对于某些j∈J~#(R)都可以表示成1+j或-1+j的形式,也可以表示为U(R)=(1+J~#(R))∪(-1+J~#(R)).这里,J~#(R)={x∈|(?)n,使得x^n∈J(R)}.证明了一个环R的弱UJ~#性在角环和S(R,σ)下是保持的.每个abelian weakly nil clean环是弱UJ~#环.如果I是环R的幂零理想,那么R/I~#是弱UJ~#环当且仅当R是弱UJ~#环.更进一步研究了clean weakly UJ~#环.如果R是clean环,那么R是弱UJ~#环当且仅当R/J(R)是弱UU环.A new class of rings is introduced.A ring R is called a weakly UJ#ring if every unit can written as1+j or-1+j,where j∈J#(R),i.e.,U(R)=(1+J#(R))∪(-1+J#(R)).Here,J#(R)={x∈R|n,such that x n∈J(R)}.These rings are shown to be a unifying generalization of corners and S(R,σ).In this article,every abelian weakly nil clean ring is weakly UJ#.If I is a nil\|ideal,then R/I is weakly UJ#if and only if so is R.Furthermore,the description of clean weakly UJ#ring is established.If R is a clean ring,then R is weakly UJ#if and only if R/J(R)is weakly UU.

关 键 词：WEAKLY UJ#环 WEAKLY UU环 WEAKLY NIL CLEAN环 CLEAN WEAKLY UJ#环 

分 类 号：O153.3[理学—数学]