IDENTITIES WITH GENERALIZED DERIVATIONS

Let R be a prime ring with extended centroid C. By a generalized derivation of R we mean an additive map g: R → R such that (xy) ^g = x^gy + xy ^δ for all x ∈ R, where δ is a derivation of R. In this paper we prove a version of Kharchenko's theorem for generalized derivations and present some results concerning certain identities with generalized derivations.