ON NIL – SEMI CLEAN RINGS

In this paper, the notions of semi-idempotent elements and nil-semiclean elements are introduced. we show that, if a ring r is a nil-semi clean ring, then the jacobson radical, j(r), of r is nil. we also characterize some properties related to orthogonal idempotent elements e and f in a ring r. we prove that if r is a nil-semi clean ring and the idempotent elements of r are central, then the jacobson radical j(r) of r equals the set of all nilpotent elements of r. finally, we show that if r is a commutative ring, then the polynomial ring r[x] is not nil-semi clean ring.