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Proceedings of the American Mathematical Society

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

 

 

Imbedding nondegenerate Jordan algebras in semiprimitive algebras


Authors: W. S. Martindale and K. McCrimmon
Journal: Proc. Amer. Math. Soc. 103 (1988), 1031-1036
MSC: Primary 17C10
MathSciNet review: 954978
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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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DOI: https://doi.org/10.1090/S0002-9939-1988-0954978-2
Article copyright: © Copyright 1988 American Mathematical Society