COMMUTATIVITY OF MULTIPLICATIVE b-GENERALIZED DERIVATIONS OF PRIME RINGS

Consider R to be an associative prime ring and K to be a nonzero dense ideal of R. A mapping (need not be additive) F : R -> Qmr associated with derivation d : R -> R is called a multiplicative b-generalized derivation if F(alpha 6) = F(alpha)6 + b alpha d(6) holds for all alpha, 6 is an element of R and for any fixed (0 6=)b is an element of Qs subset of Qmr. In this manuscript, we study the commutativity of prime rings when the map b-generalized derivation satisfies the strong commutativity preserving condition and moreover, we investigate the commutativity of prime rings that admit multiplicative b-generalized derivation, which improves many results in the literature.