Central Idempotent of Rings

Abstract

In this paper, we find several necessary conditions for the idempotents of a ring R to be central (for example: if eU_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_RÍC_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).

Keywords and phrases. Rings, Central Idempotent.

2000 Mathematics Subject Classification. XX-16