Author : B. Yass, a
Engineering and Technology Journal,
2016, Volume 34, Issue 2, Pages 328-333
Let 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.