Abstract
A classical result of Herstein asserts that any Jordan derivation on a prime ring with char(R) ≠ 2 is a derivation. It is our aim in this paper to prove the following result, which is in the spirit of Herstein’s theorem. Let R be a prime ring with char(R) = 0 or char(R) > 4, and let D: R → R be an additive mapping satisfying the relation D(x4) = D(x)x3 + xD(x2)x + x3D(x) for all x ∈ R. In this case, D is a derivation.
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