ON THE IDENTITY $h(x)=af(x)+g(x)b$

Abstract

A description of the generalized (, )-derivations f , g and h of a prime ring R which satisfying h = af + gb is given. Receently, Bresar [3] gave a description of derivations d, g and h of a prime ring R satisfying d = ag+hb, where a and b are some fixed noncentral elements of R. This results generalizes a theorem in Herstein's paper Latter on, the author [6] exteneded this result to (, )-derivations, the result we obtained generalizes several results simultaneously. In this note we will extend this result further to the so-called generalized (, )-derivations which are motivated by the same paper