ON ADDITIVE MAPS OF PRIME-RINGS SATISFYING THE ENGEL CONDITION

Let A be a prime ring with nonzero right ideal R and f : R --> A an ad ditive map. Next, let k,n(1),n(2),...,n(k) be natural numbers. Suppose that [...[[f(x),x(n1)], x(n2)],...,x(nk)] = 0 for all x is an element of R. Then it is proved in Theorem 1.1 that [f(x), x] = 0 provided th at either char(A) = 0 or char(A) > n(1)+n(2)+...+n(k). Theorem 1.1 is a simultaneous generalization of a number of results proved earlier.