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