Let be a ring and a nonempty subset of . An additive mapping is called Left generalized derivation (Left Jordan derivation) on If there exists a derivation such that respect to left Jordan generalized derivation holds for all in . Suppose that is a 2- torsion free prime ring and a non zero Lie ideal of such that in for all in. In this paper we proved that if is a left Jordan generalized derivation on , then is a left generalized derivation on
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