Abstract: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.
Keywords: semiprime ring, left centralizer, centralizer, Jordan centralizer
AMS Subject Classification: 16N60, 16W10, 16W25