Lie inner ideals are nearly Jordan inner ideals

López, Antonio

doi:10.1090/S0002-9939-2013-11809-5

Lie inner ideals are nearly Jordan inner ideals
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by Antonio Fernández López

Proc. Amer. Math. Soc. 142 (2014), 795-804

DOI: https://doi.org/10.1090/S0002-9939-2013-11809-5

Published electronically: December 4, 2013

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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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