Ayran, AyşeAydin, Neşet2025-01-272025-01-2720161311-8080https://doi.org/10.12732/ijpam.v109i4.14https://hdl.handle.net/20.500.12428/12918Let 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.eninfo:eu-repo/semantics/openAccessExtended centroid; Martindale quotient ring; Prime ring; Semigroup idealArticle109491191810.12732/ijpam.v109i4.142-s2.0-84991706736N/A