On Left s -Centralizers Of Jordan Ideals And Generalized Jordan Left (s ,t ) -Derivations Of Prime Rings


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 freeprime ring, U is a Jordan ideal of R and G is an additive mapping from R intoitself satisfying the conditionG(ur + ru) = G(u)s (r) + G(r)s (u) , for alluÎU, r ÎR . Then G(ur) = G(u)s (r) , for all uÎU, r ÎR . Also, we extend theresult of S. M. A. Zaidi, M. Ashraf and S. Ali on left (s ,s )-derivation of prime ringto Jordan ideal by introducing the concept of generalized Jordan left (s ,t )-derivation.