CENTRAL IDEMPOTENT OF RINGS

In this paper, we find several necessary conditions for the idempotents of a ring R to be central (for example: if e U_R = U_R 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 subseteq C_R then reg R = S.cl_R where reg R is the set of regular elements in R and S.cl_R is the set of strongly clean element in R).