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

Abstract

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.

Keywords

• centralizer
• derivation
• left
• generalized
• prime ring