关于Weakly UJ~#环(英)

On Weakly UJ~# Rings

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.