Jordan homomorphisms onto nondegenerate Jordan algebras
type: Item
instance of: scholarly article
title: Jordan homomorphisms onto nondegenerate Jordan algebras
zbMATH Open document ID: 0708.17027
DOI: 10.1016/0021-8693(90)90285-V
author: W. S. III Martindale
published in: Journal of Algebra
publication date: 1990-01-01T00:00:00Z
review text: Let \(\phi: J_ 0\to J\) be an epimorphism of special Jordan algebras over a field of characteristic \(\neq 2\), where \(J\) is nondegenerate. The author proves that J embeds in a direct sum \(J_ 1\oplus J_ 2\) of special Jordan algebras and that \(\phi\) lifts to a direct sum \(\phi_ 1\oplus \phi_ 2\) of homomorphisms \(\phi_ i: J_ 0\to J_ i\) such that \(\phi_ 1\) lifts to a homomorphism of associative envelopes of \(J_ 0\) and \(J_ 1\) and such that \(J_ 2\) is a Wagner algebra in the sense that \([x,y]^ 2\) is central for all x and y in \(J_ 2\). Zel'manov's work plays a key role in the proof of this theorem, which generalizes a result of McCrimmon from the case where \(J\) is prime to the case where \(J\) is nondegenerate. The generalization is based on the author's work with Baxter on central closures of semiprime nonassociative algebras.
Mathematics Subject Classification ID: 17C30
Mathematics Subject Classification ID: 17C10
zbMATH DE Number: 4163124
zbMATH Keywords: Jordan homomorphism
zbMATH Keywords: Zelmanov polynomial
zbMATH Keywords: special Jordan algebras
zbMATH Keywords: Wagner algebra
reviewed by: Robert Bix
MaRDI profile type: Publication
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full work available at URL: 0021-8693(90)90285-v
OpenAlex ID: W2014668785
description: scientific article; zbMATH DE number 4163124