A note on derivations and Jordan ideals of prime rings

Abstract

Let F : R → R be a generalized derivation of a 2-torsion free prime ring R together witha derivation d: In this paper, we show that a nonzero Jordan ideal J of R contains a nonzero ideal ofR. Further, we use this result to prove that if F([x,y]) ∈ Z(R) for all x, y ∈ J; then R is commutative.Consequently, it extends a result of Oukhtite, Mamouni and Ashraf.

Keywords

• Prime rings| Jordan ideals| Generalized derivations| Martindale ring of quotients|Generalized polynomial identities (GPIs)