Abbas Zivari-Kazempour - Department of Mathematics, Ayatollah Borujerdi University, Borujerd, Iran.

‎Let R be a ۲-torsion-free semiprime ring and \theta be an epimorphism of R‎. ‎In this paper‎, ‎under special hypotheses‎, we prove that if T‎: ‎R\longrightarrow R‎ ‎is an additive mapping such that‎‎‎‎‎‎T(xyx)=θ(x)T(y)θ(x)‎,‎‎‎‎‎holds for all x‎, ‎y\in R‎, ‎then‎ ‎T is a θ-centralizer‎either R is unital‎ or θ(Z(R))=Z(R).

semiprime ring‎, ‎centralizer‎, ‎\theta-centralizer‎, ‎epimorphism