Let d be a Jordan derivation from a ring A into an A-bimodule M. Our main result shows that the restriction of d to the ideal of A generated by certain higher commutators of A is a derivation. This general statement is used for proving that under various additional conditions d must be a derivation on A. Furthermore, several examples of proper Jordan derivations are given, C^-algebras admitting proper additive jordan derivations are characterized, and the connections with the related problems on jordan homomorphisms and jordan A-module homomorphisms are discussed.
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Matej Brešar (2005) studied this question.
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