results on generalized derivations in prime rings

A prime ring s with the centre z and generalised derivations that meet certain algebraic identities is considered. let’s assume that ψ and φ are two generalised derivations associated with ψ and φ on s, respectively. in this article, we examine the following identities: (i) ψ(a)b−aφ(b) ∈ z, (ii) ψ(a)b−bφ(a) ∈ z, (iii) ψ(a)a−bφ(b) ∈ z, (iv) ψ(a)a−aφ(b) ∈ z, (v) ψ(a)a − bφ(a) ∈ z, for every a, b ∈ j, where j is a non-zero two sided ideal of s. we also provide an example to show that the condition of primeness imposed in the hypotheses of our results is essential.