Academic Editor: Youssef EL FOUTAYENI
Received |
Accepted |
Published |
28 January 2020 |
12 February 2020 |
10 March 2020 |
Abstract: Let $N$ be a zero-symmetric prime near-ring. An additive mapping$F: N\rightarrow N$ is said to be a generalized semiderivationassociated with a semiderivation $d$ and a map $g$ if it satisfies$F(xy)=F(x)y+g(x)d(y)=d(x)g(y)+xF(y)$ and $F(g(x))=g(F(x))$ for all$x,y\in N$. The purpose of this paper is to extend some resultsconcerning generalized derivations of prime near rings togeneralized semiderivations. Moreover, example is provided to showthe necessity for $N$ to be prime and $g$ to be an automorphismin the hypothesis of the theorems. When, $g=id_{N},$ one can easilyobtain the main results of \cite{ref4} and \cite{ref7}.
