• PRIME RINGS WITH NILPOTENT DERIVATIONS

Abstract

Chung and Luh studied semiprime rings with nilpotent derivations and established the results for (n-1)! torsion free semiprime rings. Bresar generalized these results. In this paper, we prove that if d is a derivation on a semiprime ring R such that , for all , then for all x in R provided R is (n-1)! torsion free and  if R is prime, then either a=0 or b=0 or d=0. Using this result we prove that if d is a non-zero derivation on a 2- torsion free prime ring R and if  f  is an additive mapping of R such that for all x in R, then  f=0.