I. N. Herstein has shown that every Jordan derivation on a prime ring not of charactetistic 2 2 is a derivation. This result is extended in this paper to the case of any ring in which 2 x = 0 2x = 0 implies x = 0 x = 0 and which is semiprime or which has a commutator which is not a zero divisor.
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J. M. Cusack (1975) studied this question.
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