On two sided α-n-derivation in 3-prime near-rings

Abstract

Let N be a left near-ring and let α be a function of N. We introduce the notion of two sided α-n-derivation and prove that a prime zero symmetric near-ring involving α-n-derivations satisfying certain identities is a commutative ring.Also, some examples are given to shown that the 3-primeness condition in our results is not redundant.