Central idempotent of rings

Abstract EN

In this paper, we find several necessary conditions for the idempotents of a ring R to be central (for example : if eUR = UR e for every idempotent e of R then the idempotents of R are central, where U R is the set of units in R).We present some several properties of a ring whose idempotents are central (for instance : If I R ⊆ CR then reg R = S.clR where reg R is the set of regular elements in R and S.clR is the set of strongly clean element in R).