关于Weakly UJ#环

摘要

引进了一类新环:环 R是弱U J#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∈ R|? n,使得 xn∈ J(R)}.证明了一个环 R的弱U J#性在角环和 S(R,σ)下是保持的.每个abelian weakly nil clean环是弱U J#环.如果 I是环R的幂零理想,那么R/I是弱U J#环当且仅当 R是弱U J#环.更进一步研究了clean weakly U J#环.如果R是clean环,那么R是弱U J#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 as 1+ 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 xn∈ 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 U J#ring is established.If R is a clean ring,then R is weakly UJ#if and only if R/J(R)is weakly UU.