PERMUTING TRI- -DERIVATIONS IN PRIME GAMMA-NEAR-RINGS
In this paper, we define a permuting tri- -derivation and a permuting tri-generalized derivation in gamma-near-rings. Let N be a prime G-near-ring with the centre and D be a nonzero permuting tri- -derivation with the trace d of N. If then we prove that N is a commutative G-ring. If N is a 3!-torsion free and then we prove that We also prove that if F is a nonzero permuting tri-right generalized derivation of N with the trace f associated with D and then is abelian and for all
permuting, tri-deviation, tri- -derivation, gamma-near-ring.