α-N-Derivations in Prime Near - Rings

In this paper, we introduce the notion of alpha-n derivations in prime nearrings, In [3]Samman. M. S interpreted alpha -derivation of A and studied some properties of this derivation. In [1], M. Ashraf and M. A. Siddeeque interpreted n-derivation in nearing and studied some properties included there, influenced by this concept. alpha - n-derivation of nearing A.,which gives a generalization of nderivation of nearing is defined in this study. The main purpose is to show that a prime nearing A with some identities on alpha-n-derivations satisfies some important properties. Our results are generalized to many previously results on prime nearing with derivations, n-derivations and alpha- derivations, initially we begin with necessary lemmas which are essential for developing the proofs our main results. In [3] Samman M. S. proved that if d is an alpha - derivation of a prime nearringA in a way that d replace with alpha, thend2 = 0 implies d = 0 and The composition of alpha - derivations obtained, We have extended this result in the setting of an alpha - nderivation in near rings.