$(\theta,\phi)$-derivations as homomorphisms or as anti-homomorphisms on a near ring
Main Article Content
Let $N$ be a near ring. An additive mapping $d:N\longrightarrow N$ is said to be a $(\theta,\phi)$-derivation on $N$ if there exist mappings $\theta,\phi:N\longrightarrow N$ such that$d(xy)=\theta(x)d(y)+d(x)\phi(y)$ holds for all $x,y \in N$. In the context of 3-prime and 3-semiprime nearrings, we show that for suitably-restricted $\theta$ and $\phi$, there exist no nonzero $(\theta,\phi)$-derivations which act as a homomorphism or an anti-homomorphism on $N$ or a nonzero semigroup ideal of $N$.
How to Cite
Ali, A., Bell, H. E., & Rani, R. (2012). $(\theta,\phi)$-derivations as homomorphisms or as anti-homomorphisms on a near ring. Tamkang Journal of Mathematics, 43(3), 385–390. https://doi.org/10.5556/j.tkjm.43.2012.849
M. Ashraf, Ali Asma and Ali Shakir, ($sigma,tau$)-derivations on prime near rings, Arch. Math., 40(2004), 281--286.
A. Ali, N. Rehman and A. Shakir, On Lie ideals with derivations as homomorphisms and anti-homomorphisms, Acta Math. Hungar., 101(2003), 79--82.
H. E. Bell, On derivations in near rings II, Kluwer Academic Publ. Math. Appl. Dordr., 426(1997), 191--197.
H. E. Bell and L. C. Kappe, Rings in which derivations satisfy certain algebraic conditions, Acta. Math. Hungar., 53(1989), 339--346.
X. K. , Wang, Derivations in prme near rings, proc. Amer. Math. Soc., 121(1994), 361--366.