Generalized derivations with Engel condition on Lie ideals of prime rings.

Consider ℜ as a prime ring which is non-commutative in structure with a suitable characteristic. Here, 풵 ⁢ (ℜ) is the center of ℜ and 풬 is the Utumi ring of quotients where 풞 is the extended centroid of ℜ . Suppose 풫 to be a Lie ideal of ℜ which is non-central. Let 풦 be a generalized derivation of ℜ related with derivation μ of ℜ . If 풦 satisfies certain typical algebraic identities, then we prove that 풦 is either the identity map or the zero map or the scalar map and further information is also drawn on the associated scalar unless ℜ embeds in M 2 ⁢ (풞) , a matrix ring of order 2 × 2 over 풞 . [ABSTRACT FROM AUTHOR]