右半Duo　Л－正则环

RIGHT SEMI-DUO Л-REGULAR RINGS

本文的目的是推广Ｂａｄａｕｉ的结果，假定Ｒ是右半Ｄｕｏ环，我们证明了：（１）Ｒ是Л－正则环当且仅当Ｒ是单位Л－正则环；（２）Ｒ是强Л－正则环当且仅当对任意ａ∈Ｒ存在ｅ∈Ｉｄ（Ｒ），ｕ∈Ｕ（Ｒ）和ｂ∈Ｋ（Ｒ）使ａ＝ｅｕ＋ｂ；（３）Л－正则环的每一个元素是Ｒ中两个可逆元素之和当且仅当Ｒ中每个幂等元是Ｒ的两个可逆元素之和．

The aim of this paper is to extend Badawi's results. Let R be a right semi-duo ring, we prove the following results:(1) R is a Л-regular ring if and only if R is unit Л-regular;(2)R is strongly π-regular if and only if any a ∈R there exists e ∈Id(R),u∈U(R) and b ∈ K(R) such that α=eu+b;(3) Every idempotent in a Л-regular ring R is a sum of two units of R if and onlv if everv element in R is a sum of two units of R.