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Biadditive mappings B: R x R -> R where R is a prime ring with certain additional properties, satisfying B(x, x)x = xB(x, x) for all x R, are characterized. As an application we determine the structures of commutativity-preserving mappings, Lie isomorphisms, and Lie derivations of certain prime rings.
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Matej Brešar (1993) studied this question.
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