On left σ-centralizers of Jordan ideals and generalized Jordan left (σ, t)‎ -derivations of prime rings

الملخص EN

In this paper we generalize the result of S.

Ali and C.

Heatinger on left s - centralizer of semiprime ring to Jordan ideal, we proved that if R is a 2-torsion free prime ring, U is a Jordan ideal of R and G is an additive mapping from R into itself satisfying the conditionG(ur + ru) = G(u)s (r) + G(r)s (u) , for all uÎU, r ÎR .

Then G(ur) = G(u)s (r) , for all uÎU, r ÎR .

Also, we extend the result of S.

M.

A.

Zaidi, M.

Ashraf and S.

Ali on left (s ,s )-derivation of prime ring to Jordan ideal by introducing the concept of generalized Jordan left (s ,t )- derivation