International Mathematical Forum, 2, 2007, no. 57, 2823 - 2829 On Jordan Generalized k -Derivations of 2-Torsion Free Prime Γ N -Rings Sujoy Chakraborty Department of Mathematics Shah Jalal University of Science and Technology Sylhet-3114, Bangladesh sujoy chbty@yahoo.com Akhil Chandra Paul Department of Mathematics Rajshahi University Rajshahi-6205, Bangladesh acpaul math@yahoo.com 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. Mathematics Subject Classification: Primary 16N60, Secondary 16W25, 16U80 Keywords: Derivation and generalized derivation, k -derivation and gener- alized k -derivation, Jordan k -derivation and Jordan generalized k -derivation, gamma ring, semiprime and prime gamma rings 1 Introduction Let M and Γ be two additive abelian groups. If there exists a mapping (a, α, b) → aαb of M × Γ × M → M satisfying the following for all a, b, c ∈ M and α, β ∈ Γ: