Geodesic
Centralizers on semiprime rings
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 2, pp. 237-245

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The main result: Let $R$ be a $2$-torsion free semiprime ring and let $T:R\rightarrow R$ be an additive mapping. Suppose that $T(xyx) = xT(y)x$ holds for all $x,y\in R$. In this case $T$ is a centralizer.
Classification : 16A12, 16A68, 16A72, 16N60, 16W10, 16W20
Keywords: prime ring; semiprime ring; derivation; Jordan derivation; Jordan triple derivation; left (right) centralizer; left (right) Jordan centralizer; centralizer 
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Vukman, Joso. Centralizers on semiprime rings. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 2, pp. 237-245. http://geodesic.mathdoc.fr/item/CMUC_2001__42_2_a1/