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Keywords:
prime ring; semiprime ring; derivation; Jordan derivation; left (right) centralizer; left (right) Jordan centralizer
prime ring; semiprime ring; derivation; Jordan derivation; left (right) centralizer; left (right) Jordan centralizer
Summary:
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.
References:
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