Lie inner ideals are nearly Jordan inner ideals
In this note we extend the Lie
inner ideal structure of simple Artinian rings developed by
Benkart to centrally closed prime algebra A. New Lie inner
ideals (which we call non-standard) occur when making this
extension. A necessary and sufficient condition for A to have a
non-standard inner ideal is the existence in A of a zero square
element which is not von Neumann regular.
(This paper has appeared in Proc. Amer. Math. Soc. 142 (2014), 795--804)
A. Fernández López < emalfer@uma.es >