On Prime-Gamma-Near-Rings with Generalized Derivations

Let be a 2-torsion free prime Γ-near-ring with center (). Let (,) and (,？) be two generalized derivations on . We prove the following results: (i) if ([,])=0 or ([,])=±[,] or 2()∈() for all ,∈, ∈Γ, then is a commutative Γ-ring. (ii) If ∈ and [(),]=0 for all ∈, ∈Γ, then ()∈(). (iii) If (,？) acts as a generalized derivation on , then =0 or =0.