【摘要】 每个单位正则环都是c lean环,但每个单位正则环是否是强c lean环?它至今仍是一个没有解决的问题。本文通过对单位正则环的内部h结构进一步研究,给这个公开问题局部回答。我们得到:设R是单位正则环,设E为R的非平凡幂等元集,且2U(R)。则下列等价:(1)R是强c lean环;(2)H C(V(R));(3)N C(U(R))。更多还原

【Abstract】 Every unit regular ring is clean ring.Is every unit regular ring strongly clean? It is still an open question.This paper gives a partial answer to this open question through further study on the internal structure of unit regular ring.We draw α conclusion: Let R be unit-regular ring.Let E be the set of nontrivial idempotent in R,and 2C(U(R)).Then the following is equivalent:(1)R is strongly clean ring;(2)HC(U(R);(3)NC(U(R)).更多还原