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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:
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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