SOME SPECIAL CLASSES OF 3-PRIME NEAR-RINGS INVOLVING MULTIPLICATIVE DERIVATIONS

This research work investigate some new results on near-rings through multiplicative derivations and present the commutativity of a 3-prime near-ring satisfying some differential and algebraic identities on nonzero Jordan ideals of 2-torsion free zero symmetric involving multiplicative derivations by considering two derivations instead of one derivation and established that if R is a 2-torsion free prime ring admitting a strong commutativity preserving (SCP) derivation d. Further, proved that if J is a nonzero Jordan ideal of a 2-torsion free zero symmetric together with 3-prime near-ring N and d1, d2 are two nonzero derivations on N such that d2  is commuting on J then either d1=0 on J or N is a multiplicative commutative near-ring and also prove some result on special class of near-rings with suitable constraints of its subsets.