Some commutativity criteria involving endomorphism conditions on prime ideals

In this paper we initiate a new approach consisting to characterize the commutativity of a quotient ring $R/P$ by endomorphisms of $R$ satisfying some algebraic identities involving the prime ideal $P.$ Some well-known results concerning the commutativity of prime insert ignore into journalissuearticles values(semi-prime); rings have been improved.