On nil – semi clean rings

Abstract EN

In this paper, the notions of semi-idempotent elements and nil-semi clean 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 Rare 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.