# Article

 Title: An identity related to centralizers in semiprime rings (English) Author: Vukman, Joso Language: English Journal: Commentationes Mathematicae Universitatis Carolinae ISSN: 0010-2628 (print) ISSN: 1213-7243 (online) Volume: 40 Issue: 3 Year: 1999 Pages: 447-456 . Category: math . 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. (English) Keyword: prime ring Keyword: semiprime ring Keyword: derivation Keyword: Jordan derivation Keyword: left (right) centralizer Keyword: left (right) Jordan centralizer MSC: 16A12 MSC: 16A68 MSC: 16A72 MSC: 16N60 MSC: 16R50 MSC: 16W10 MSC: 16W20 idZBL: Zbl 1014.16021 idMR: MR1732490 . Date available: 2009-01-08T18:54:03Z Last updated: 2012-04-30 Stable URL: http://hdl.handle.net/10338.dmlcz/119101 . Reference: [1] Brešar M., Vukman J.: Jordan derivations on prime rings.Bull. Austral. Math. Soc. 37 (1988), 321-323. MR 0943433 Reference: [2] Brešar M.: Jordan derivations on semiprime rings.Proc. Amer. Math. Soc. 104 (1988), 1003-1006. MR 0929422 Reference: [3] Cusak J.: Jordan derivations on rings.Proc. Amer. Math. Soc. 53 (1975), 321-324. MR 0399182 Reference: [4] Herstein I.N.: Jordan derivations in prime rings.Proc. Amer. Math. Soc. 8 (1957), 1104-1110. MR 0095864 Reference: [5] Herstein I.N.: Rings with involution.Chicago Lectures in Math., Univ. of Chicago Press, Chicago, London, 1976. Zbl 0495.16007, MR 0442017 Reference: [6] Posner E.: Derivations in prime rings.Proc. Amer. Math. Soc. 8 (1957), 1093-1100. MR 0095863 Reference: [7] Vukman J.: Centralizers in prime and semiprime rings.Comment. Math. Univ. Carolinae 38 (1997), 231-240. MR 1455489 Reference: [8] Zalar B.: On centralizers of semiprime rings.Comment. Math. Univ. Carolinae 32 (1991), 609-614. Zbl 0746.16011, MR 1159807 .

## Files

Files Size Format View
CommentatMathUnivCarolRetro_40-1999-3_5.pdf 174.8Kb application/pdf View/Open

Partner of