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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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Keywords: Jordan algebra, minimum condition, quadratic ideal, nil ideal, radical, nilpotence, Peirce decomposition
Article copyright: © Copyright 1971 American Mathematical Society