A result on generalized derivations on right ideals of prime rings - Argaç, N.; Demir, Ç. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
Let R be a prime ring of characteristic not 2 and let I be a nonzero right ideal of R. Let U be the right Utumi quotient ring of R and let C be the center of U. If G is a generalized derivation of R such that [[G(x), x], G(x)] = 0 for all x I, then R is commutative or there exist a, b U such that G(x) = ax + xb for all x R and one of the following assertions is true: (1)(a - λ)I = (0) = (b + λ)I for some λ C, (2)(a - λ)I = (0) for some λ C and b C.