%0 Journal Article
%T $( heta,phi)$-derivations as homomorphisms or as anti-homomorphisms on a near ring
%A Asma Ali
%A Howard E. Bell
%A Rekha Rani
%J Tamkang Journal of Mathematics
%D 2012
%I Tamkang University
%R 10.5556/j.tkjm.43.2012.385-390
%X Let $N$ be a near ring. An additive mapping $d:Nlongrightarrow N$ is said to be a $( heta,phi)$-derivation on $N$ if there exist mappings $ heta,phi:Nlongrightarrow N$ such that$d(xy)= heta(x)d(y)+d(x)phi(y)$ holds for all $x,y in N$. In the context of 3-prime and 3-semiprime nearrings, we show that for suitably-restricted $ heta$ and $phi$, there exist no nonzero $( heta,phi)$-derivations which act as a homomorphism or an anti-homomorphism on $N$ or a nonzero semigroup ideal of $N$.
%K 3-prime and 3-semiprime nearrings
%K (theta
%K phi)-derivations
%U http://journals.math.tku.edu.tw/index.php/TKJM/article/view/849