α-N-derivations in prime near – rings

Abstract

In this paper, we introduce the notion of α-n derivations in prime nearrings, In [3]Samman. M.S interpreted α-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. α-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 α-n-derivations satisfies some important properties. Our results are generalized to many previously results on prime nearing with derivations, n-derivations and α-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 α – derivation of a prime nearringA in a way that d replace with α, then d2 = 0 implies d = 0 and The composition of α – derivations obtained, We have extended this result in the setting of an α - nderivation in near rings.In this paper, we introduce the notion of α-n derivations in prime nearrings, In [3]Samman. M.S interpreted α-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. α-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 α-n-derivations satisfies some important properties. Our results are generalized to many previously results on prime nearing with derivations, n-derivations and α-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 α – derivation of a prime nearringA in a way that d replace with α, then d2 = 0 implies d = 0 and The composition of α – derivations obtained, We have extended this result in the setting of an α -...