A near-ring is an extension of the ring without having to fulfill the commutative of the sum and left distributive of the addition and multiplication operations. This paper shows that a prime and zero symmetric near-ring with derivation on near-ring satisfies proposed conditions is a commutative ring.

Near-ring is an extension of ring without having to fulfill a commutative of the addition operations and left distributive of the addition and multiplication operations It has been found that some theorems related to a prime near-rings are commutative rings involving the derivation of the Lie products and the derivation of the Jordan product. The contribution of this paper is developing the previous theorem by inserting derivations to the Lie products and the Jordan product. Keywords: Derivation, Prime Near-Ring, Lie Products and Jordan Products.