International Journal of Algebra, Vol. 6, 2012, no. 23, 1127 - 1134 Orthogonal Generalized Derivations in Semiprime Gamma Near-Rings 1 Kalyan Kumar Dey, 2 Akhil Chandra Paul and 3 Isamiddin S. Rakhimov 1, 2 Department of Mathematics, Rajshahi University, Rajshahi-6205, Bangladesh 3 Department of Mathematics, FS, & Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, Malaysia 1 kkdmath@yahoo.com 2 acpaulru_math@yahoo.com 3 risamiddin@gmail.com Abstract Let N be a 2-torsion free semiprime Γ-near-ring and let D,G be two generalized derivations on N. In this paper, we define orthogonality of two generalized derivations in Γ-near-rings. If D and G are orthogonal on N then we prove that DG is a generalized derivation on N and either DG or GD is a left centralizer of N. We also prove that if D 2 = 0 then D = 0. Mathematics Subject Classification: 16A70, 16N60, 16W25 Keywords: Semiprime Γ-near-ring, Derivation, Generalized Derivation Orthogonal derivation, Orthogonal generalized derivation 1. Introduction A Γ-near-ring is a triple (N, +, Γ) where (i) (N, +) is a not necessarily abelian group , (ii) Γ is a non-empty set of binary operations on N such that for each α∈Γ,