## Joso Vukman

*An identity related to centralizers in semiprime rings *

Comment.Math.Univ.Carolinae 40,3 (1999) 447-456. **Abstract:**The purpose of this paper is to prove the following result: Let $R$ be a $2$-torsion free semiprime ring and let $T:R\rightarrow R$ be an additive mapping, such that $2T(x^2)=T(x)x+xT(x)$ holds for all $x\in R$. In this case $T$ is left and right centralizer.

**Keywords:** prime ring, semiprime ring, derivation, Jordan derivation, left (right) centralizer, left (right) Jordan centralizer

**AMS Subject Classification:** 16A12, 16A68, 16A72

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