# Article

 Title: On centralizers of semiprime rings (English) Author: Zalar, Borut Language: English Journal: Commentationes Mathematicae Universitatis Carolinae ISSN: 0010-2628 (print) ISSN: 1213-7243 (online) Volume: 32 Issue: 4 Year: 1991 Pages: 609-614 . Category: math . Summary: 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. (English) Keyword: semiprime ring Keyword: left centralizer Keyword: centralizer Keyword: Jordan centralizer MSC: 16N60 MSC: 16U70 MSC: 16W10 MSC: 16W20 MSC: 16W25 idZBL: Zbl 0746.16011 idMR: MR1159807 . Date available: 2009-01-08T17:47:29Z Last updated: 2012-04-30 Stable URL: http://hdl.handle.net/10338.dmlcz/118440 . Reference: [1] Brešar M., Vukman J.: On some additive mapping in rings with involution.Aequationes Math. 38 (1989), 178-185. MR 1018911 Reference: [2] Brešar M., Zalar B.: On the structure of Jordan $\ast$-derivations.Colloquium Math., to appear. MR 1180629 Reference: [3] Herstein I.N.: Topics in ring theory.University of Chicago Press, 1969. Zbl 0232.16001, MR 0271135 Reference: [4] Herstein I.N.: Theory of rings.University of Chicago Press, 1961. Reference: [5] Johnson B.E., Sinclair A.M.: Continuity of derivations and a problem of Kaplansky.Amer. J. Math. 90 (1968), 1067-1073. Zbl 0179.18103, MR 0239419 Reference: [6] Šemrl P.: Quadratic functionals and Jordan $\ast$-derivations.Studia Math. 97 (1991), 157-165. MR 1100685 .

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