On additive maps of prime rings satisfying the engel condition

Abstract

Let A be a prime ring with nonzero right ideal R and f : R → A an additive map. Next, let k,n1, n2,…,nk be natural numbers. Suppose that […[[(x), xn1], xn2],…, xnk]=0 for all x ∈ R. Then it is proved in Theorem 1.1 that [f(x),x]=0 provided that either char(A)=0 or char (A)> n1+n2+ …+nk Theorem 1.1 is a simultaneous generalization of a number of results proved earlier.