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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Jordan algebras with minimum condition


Author: David L. Morgan
Journal: Trans. Amer. Math. Soc. 155 (1971), 161-173
MSC: Primary 17.40
MathSciNet review: 0276290
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Abstract: Let $ J$ be a Jordan algebra with minimum condition on quadratic ideals over a field of characteristic not 2. We construct a maximal nil ideal $ R$ of $ J$ such that $ J/R$ is a direct sum of a finite number of ideals each of which is a simple Jordan algebra. $ R$ must have finite dimension if it is nilpotent and this is shown to be the case whenever $ J$ has ``enough'' connected primitive orthogonal idempotents.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0276290-1
PII: S 0002-9947(1971)0276290-1
Keywords: Jordan algebra, minimum condition, quadratic ideal, nil ideal, radical, nilpotence, Peirce decomposition
Article copyright: © Copyright 1971 American Mathematical Society