On a certain functional identity in prime rings. II.

Brešar, M.; Chebotar, M.A.

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The purpose of this paper is to prove the following result: Let $R$ be a $2$ -torsion free semiprime ring and let $T : R \to R$ be an additive mapping, such that $2 T (x^{2}) = T (x) x + x T (x)$ holds for all $x \in R$ . In this case $T$ is left and right centralizer.