Imbedding nondegenerate Jordan algebras in semiprimitive algebras

Martindale, W. S.; McCrimmon, K.

doi:10.1090/S0002-9939-1988-0954978-2

Imbedding nondegenerate Jordan algebras in semiprimitive algebras
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by W. S. Martindale and K. McCrimmon PDF

Proc. Amer. Math. Soc. 103 (1988), 1031-1036 Request permission

Abstract:

Zelmanov’s structure theory for prime Jordan algebras works directly with semiprimitive algebras, and the results are extended to nondegenerate algebras using properties of the free Jordan algebra. Here we show how Amitsur’s direct power trick of imbedding $J$ in the algebra of all sequences from $J$ can be used to imbed any nondegenerate algebra $J$ in a semiprimitive $\bar J$ having exactly the same polynomial identities as $J$.

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