ON RIGHT IDEALS AND DERIVATIONS IN PRIME RINGS WITH ENGEL CONDITION

Let R be an associative ring with center Z(R) and d a nonzero derivation of R. The main object in this paper is to study the situation [[d(x(r))x(n),x(r)]s, [y, d(y)]t](m) is an element of Z(R) for all x, y in some appropriate subset of R, where n >= 0, s >= 0, t >= 0, m >= 1, r >= 1 are fixed integers and R is a prime or semiprime ring.