University of Technology-IraqEngineering and Technology Journal1681-690034220160128Commutativity Results on Prime Rings With Generalized Derivations328333112665ENA. H. MajeedShaimaa B. YassJournal Article20160101Let R be a prime ring. For nonzero generalized derivations F and G associated with the same derivation d, we prove that if d≠0, then R is commutative, if any one of the following conditions hold: (1) [F(x), G(y)] 0, (2) F(x)oG(y) 0, (3) F(x)oG(y) xoy, (4) [F(x), G(y)] [x, y], (5) [F(x), G(y)] xoy, (6) F(x)oG(y) [x, y], for all x, y R, where F will always denote onto map.https://etj.uotechnology.edu.iq/article_112665_d7255940a5011c3507e2a3fa6b24cd76.pdf