On Jordan generalized k-derivations of 2-torsion free prime \Gamma_N-rings

Abstract

In this article, we develop some important results relating to the concepts of generalized k-derivation and Jordan generalized k-derivation of certain gamma rings. Though every generalized k-derivation of a gamma ring M is obviously a Jordan generalized k-derivation of M, but the converse statement is in general not true. Here we prove that every Jordan generalized k-derivation of a 2-torsion free prime gamma ring (in the sense of Nobusawa) is a generalized k-derivation.