强J-clean环的推广

The Generalization of Strongly J-clean Rings

作为强J-clean环的推广,本文引入强J~#-clean环的概念,将强J-clean环的性质推广到强J~#-clean环上.设R为环,主要得到了:(1)a,b∈R.若ab是强J~#-clean元,则ba也是强J~#-clean元;(2)a∈R是强J~#-clean元当且仅当a是强clean元且a-a2∈J~#(R);(3)f2=f∈R,a∈fRf是R中的强J~#-clean元当且仅当a是环fRf中的强J~#-clean元.

As the generalization of strongly J-clean rings,in this article,we introduce the concept of strongly J~#-clean rings and extend the properties of strongly J-clean rings to strongly J~#-clean rings.Let Rbe a ring,we main obtain:(1)For any a,b∈R,if abis strongly J~#-clean,then so is ba;(2)a ∈ R is strongly J~#-clean if and only if ais strongly clean and a-a2∈J~#(R);(3)f∈Ris an idempotent,then a∈fRfis strongly J~#-clean in Rif and only if ais strongly J~#-clean in fRf.