Elements in one-sided unit regular rings

摘要

Let R be regular. We show that the following are equivalent:(1) R is a one sided unit regular ring. (2) For every x #x20AC; R, there exist an idempotente and a right or left invertible u such that x d eu or x d ue. (3) For every x #x20AC; R,there exists a right or left invertible u such that xu or ux is an idempotent. Moreover, we give some characterizations of one-sided unit regular rings by group inverses.