$(\alpha, \tau )$-$P$-derivations on left near-rings

Abstract

Suppose that $\mathcal{N}$ is a near-ring and $P$ is a $3$-prime ideal of $\mathcal{N}$. In this paper we introduce the notion of $(\alpha, \tau )$-$P$ derivation in near-rings, we also study the structure of the quotient near-ring $\mathcal{N}/P$ which satisfies certain algebraic identities involving $(\alpha, \tau )$-$P$ derivations.