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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A characterization of the elements of the socle of a Jordan algebra


Authors: Antonio Fernández López and Eulalia García Rus
Journal: Proc. Amer. Math. Soc. 108 (1990), 69-71
MSC: Primary 17C10; Secondary 16A34, 17C65
DOI: https://doi.org/10.1090/S0002-9939-1990-0991702-0
MathSciNet review: 991702
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Abstract: Let $J$ be a nondegenerate Jordan algebra over a field $K$ of characteristic not 2 . Here we prove that an element $b \in J$ is in the socle if and only if $J$ satisfies dcc on all principal inner ideals ${U_y}J,y \in Kb + {U_b}J$. By using this result we show that the socle of a quadratic extension ${J_F}$ of $J$ coincides with the quadratic extension ${\text {Soc(}}J{)_F}$ of its socle.


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Article copyright: © Copyright 1990 American Mathematical Society