Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4588963 | Journal of Algebra | 2007 | 10 Pages |
Abstract
In this paper we prove that a Lie algebra L is strongly prime if and only if [x,[y,L]]≠0 for every nonzero elements x,y∈L. As a consequence, we give an elementary proof, without the classification theorem of strongly prime Jordan algebras, of the fact that a linear Jordan algebra or Jordan pair T is strongly prime if and only if {x,T,y}≠0 for every x,y∈T. Moreover, we prove that the Jordan algebras at nonzero Jordan elements of strongly prime Lie algebras are strongly prime.
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Physical Sciences and Engineering
Mathematics
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