Abstract
Let R be a prime ring containing a nontrivial idempotent. Suppose that a mapping δ : R → R satisfies for all a, b ∈ R. Then there exists a z a,b (depending on a and b) in its centre Z(R) such that Moreover, if R is 2-torsion free additionally, then δ is of the form D + τ, where D is a derivation of R into its central closure T and τ is a mapping of R into its extended centroid C such that τ(a + b) = τ(a) + τ(b) + z a,b and τ([a, b]) = 0 for all a, b ∈ R
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