Local PI theory of Jordan systems
type: Item
instance of: scholarly article
title: Local PI theory of Jordan systems
zbMATH Open document ID: 0990.17025
author: Fernando Montaner
published in: Journal of Algebra
publication date: 2002-08-11T00:00:00Z
review text: Let \(x\) be an element in a Jordan system (algebra, pair or triple system). When the local algebra at \(x\) is a PI-algebra, the author says that \(x\) is a PI-element. In this paper it is proved that in a nondegenerate Jordan system the set of the PI-elements is an ideal. First the result is shown in the primitive case. Moreover, under the last assumption it is proved that when this ideal is nonzero then it coincides with the socle.
Mathematics Subject Classification ID: 17C05
Mathematics Subject Classification ID: 17C10
zbMATH DE Number: 1309258
zbMATH Keywords: Jordan system
zbMATH Keywords: Jordan algebra
zbMATH Keywords: Jordan pair
zbMATH Keywords: nondegenerate Jordan system
zbMATH Keywords: local algebra
zbMATH Keywords: PI-elements
zbMATH Keywords: ideal
reviewed by: José Antonio Cuenca Mira
MaRDI profile type: Publication
full work available at URL: jabr.1998.7755
OpenAlex ID: W2083151157
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DOI: 10.1006/JABR.1998.7755
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description: scientific article; zbMATH DE number 1309258