Generalized derivations and commutativity of prime rings

The concept of derivations as well as of generalized inner derivations (i.e. I-a,I- b (x) = ax + xb, for fixed a, b is an element of R) have been generalized as : an additive function F: R --> R satisfying F (xy) = F (x) y + xd (y) for all x, y is an element of R. where d is a derivation on R. Such a function F is said to be a generalized derivation. In the present paper we have discussed the commutativity of prime rings admitting a generalized derivation F satisfying F([x,y])=[x,y] for each pair x, y of elements in a specified subset of R.