Generalized Derivations in Prime near Rings

Let NP be a zero symmetric prime near ring with multiplicative centre Z. Let f NP NP be a generalized derivation de ned on NP. We prove that “If f 0 generalized derivation on NP for which a f NP Z b f x ,f y = 0 x,y NP ” Also if NP is 2 torsion free then NP is commutative ring, from which Herstein 2 Theorem comes out as a corollary. Dr. K. L. Kaushik "Generalized Derivations in Prime near Rings" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-6 , October 2020, URL: https://www.ijtsrd.com/papers/ijtsrd33600.pdf Paper Url: https://www.ijtsrd.com/mathemetics/algebra/33600/generalized-derivations-in-prime-near-rings/dr-k-l-kaushik