Jordan -centralizers of prime and semiprime rings

الملخص EN

The purpose of this paper is to prove the following result : Let R be a 2-torsion free ring and T : RR an additive mapping such that T is left (right) Jordan -centralizers on R.

Then T is a left (right)-centralizer of R, if one of the following conditions hold (i) R is a semi prime ring has a commentator which is not a zero divisor.

(ii) R is a non-commutative prime ring.

(iii) R is a commutative semi prime ring, where be subjective endomorphism of R.

It is also proved that if T (xy) = T (x) (y) = (x) T (y) for all x, y R and -centralizers of R coincide under same condition and (Z (R)) = Z).