Some results on semigroup ideals in prime ring with derivations

Let R be a prime ring, I be a nonzero semigroup ideal of R, d, g, h be derivations of R and a, b ? R. It is proved that if d(x) = ag(x)+h(x)b for all x ? I and a, b are not in Z(R) then there exists for some ? ? C such that h(x) = ? [a, x], g(x) = ? [b, x] and d(x) = ? [ab, x] for all x ? I. © 2016 Academic Publications, Ltd.