Tamkang Journal of Mathematics, vol.51, no.1, 2020 (Peer-Reviewed Journal)
Let N be a 2-torsion free 3-prime left near-ring with multiplicative center Z, I be a nonzero semigroup ideal of N and f be a right generalized (sigma, tau)-derivation on N associated with a (sigma, tau)-derivation d. Assume d sigma = sigma d, d tau = tau d, f sigma = sigma f, f tau = tau f. We prove that N is a commutative ring or d = 0 if any one of the following holds: i) f(N) subset of Z ii) f(I) subset of Z. Moreover, if f is a generalized (sigma, tau) derivation on N associated with d, then d = 0 if any one of the following is satisfied : iii) f acts as a homomorphism on I iv) f acts as an anti-homomorphism on I.