Geodesic
Centralizers on prime and semiprime rings
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 2, pp. 231-240.

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The purpose of this paper is to investigate identities satisfied by centralizers on prime and semiprime rings. We prove the following result: Let $R$ be a noncommutative prime ring of characteristic different from two and let $S$ and $T$ be left centralizers on $R$. Suppose that $[S(x),T(x)]S(x)+S(x)[S(x),T(x)]=0$ is fulfilled for all $x\in R$. If $S\neq 0$ $(T\neq 0)$ then there exists $\lambda $ from the extended centroid of $R$ such that $T=\lambda S$ $(S=\lambda T)$.
Classification : 16A12, 16A68, 16A72, 16N60, 16U70, 16W10, 16W25
Keywords: prime ring; semiprime ring; extended centroid; derivation; Jordan derivation; left (right) centralizer; Jordan left (right) centralizer; commuting mapping; centralizing mapping 
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     title = {Centralizers on prime and semiprime rings},
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Vukman, Joso. Centralizers on prime and semiprime rings. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 2, pp. 231-240. http://geodesic.mathdoc.fr/item/CMUC_1997__38_2_a2/