Geodesic
An identity related to centralizers in semiprime rings
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 3, pp. 447-456.

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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 $T:R\rightarrow R$ 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.
Classification : 16A12, 16A68, 16A72, 16N60, 16R50, 16W10, 16W20
Keywords: prime ring; semiprime ring; derivation; Jordan derivation; left (right) centralizer; left (right) Jordan centralizer 
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Vukman, Joso. An identity related to centralizers in semiprime rings. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 3, pp. 447-456. http://geodesic.mathdoc.fr/item/CMUC_1999__40_3_a4/