Strong commutativity preserving biderivations on prime rings

Abstract

In the present paper we investigate the commutativity in a prime ring R which admits biderivation D : R×R → R satisfying [D(x,x),D(y,y)] = [x,y] for all x,y ∈ R. More precisely, we generalize the result of Bell et.al.[3] on strong commutativity preserving biderivations. Moreover, we obtain that generalized biderivation acts as left bimultiplier, whenever it behaves as right R-homomorphisms.