• 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.
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