Abstract: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.
Keywords: prime ring, semiprime ring, derivation, Jordan derivation, Jordan triple derivation, left (right) centralizer, left (right) Jordan centralizer, centralizer
AMS Subject Classification: 16A12, 16A68, 16A72