ON GENERALIZED -HIGHER DERIVATIONS AND GENERALIZED -HIGHER DERIVATIONS OF PRIME RINGS

Abstract

Let be a Lie ideal of a 2-torsion free prime ring and be commuting endomorphisms of . In this paper we generalize the main result of M. Ashraf, A. Khan and C. Heatinger on -higher derivation of prime ring to generalized -higher derivation of Lie ideal by introducing the concept of generalized -higher derivation. Under some conditions we prove that a Jordan generalized -higher derivation of is either a generalized -higher derivation of or and every Jordan generalized -higher derivation of is a generalized -higher derivation of . Also, we generalize this result to generalized -higher derivation by introducing the concepts of -higher derivation and generalized -higher derivation. Under some conditions we prove that if is a generalized -higher derivation of , then , for all