Geodesic
On centralizers of semiprime rings
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 4, pp. 609-614.

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Let $\Cal K$ be a semiprime ring and $T:\Cal K\rightarrow \Cal K$ an additive mapping such that $T(x^2)=T(x)x$ holds for all $x\in \Cal K$. Then $T$ is a left centralizer of $\Cal K$. It is also proved that Jordan centralizers and centralizers of $\Cal K$ coincide.
Classification : 16N60, 16U70, 16W10, 16W20, 16W25
Keywords: semiprime ring; left centralizer; centralizer; Jordan centralizer 
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     title = {On centralizers of semiprime rings},
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Zalar, Borut. On centralizers of semiprime rings. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 4, pp. 609-614. http://geodesic.mathdoc.fr/item/CMUC_1991__32_4_a2/