Jordan algebras with minimum condition

Morgan, David L.

doi:10.1090/S0002-9947-1971-0276290-1

Jordan algebras with minimum condition
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by David L. Morgan PDF

Trans. Amer. Math. Soc. 155 (1971), 161-173 Request permission

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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