Generalization of Posner’s theorems

In this paper we generalize Posner’s first theorem to a 3-prime near-ring with a (?,?)-derivation. We prove that a prime ring with a non-zero (?,?)-derivation is commutative if ?(x)d(x) = d(x)t(x) for all x ? U where U is a suitable subset of R. Also, we generalize Posner’s second theorem completely to a prime ring with a (?,?)-derivation and partially to a prime ring with a (?,?)-derivation.