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Lie inner ideals are nearly Jordan inner ideals


Author: Antonio Fernández López
Journal: Proc. Amer. Math. Soc. 142 (2014), 795-804
MSC (2010): Primary 17B60, 17C50; Secondary 16N60
Published electronically: December 4, 2013
MathSciNet review: 3148514
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Abstract: In this note we extend the Lie inner ideal structure of simple Artinian rings developed by Benkart to centrally closed prime algebras $ A$. New Lie inner ideals, which we call nonstandard, occur when making this extension. A necessary and sufficient condition for $ A$ to have a nonstandard inner ideal is the existence in $ A$ of a zero square element which is not von Neumann regular. Our main tool is a theorem due to Martindale and Miers on the iterates of the derivations of prime rings.


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Additional Information

Antonio Fernández López
Affiliation: Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, 29071, Málaga, Spain
Email: emalfer@uma.es

DOI: https://doi.org/10.1090/S0002-9939-2013-11809-5
Keywords: Central closed prime algebra, Jordan-Lie inner ideal
Received by editor(s): November 17, 2011
Received by editor(s) in revised form: April 9, 2012
Published electronically: December 4, 2013
Additional Notes: The author was supported in part by the MEC and Fondos FEDER, MTM2010-19482
Dedicated: Dedicated to Professor Georgia Benkart
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2013 American Mathematical Society