b-Generalized Derivations on Prime Rings

Let R be a prime ring with center Z(R), right Martindale quotient ring Q, and extended centroid C. A b-generalized derivation is defined as an additive mapping g: R → Q such that g(xy) = g(x)y + bxd(y) for all x, y ∈ R, where b ∈ Q and d : R → Q is an additive map. We extend some well-known results concerning (generalized) derivations on prime rings to b-generalized derivations. Further, we investigate the b-generalized derivation acting as a homomorphism or anti-homomorphism in a prime ring.