Local inheritance in Jordan algebras
type: Item
instance of: scholarly article
title: Local inheritance in Jordan algebras
zbMATH Open document ID: 0824.17031
DOI: 10.1007/BF01197216
author: Teresa Cortés
author: Fernando Montaner
author: José A. Anquela
published in: Archiv der Mathematik
publication date: 1995-11-15T00:00:00Z
review text: The authors prove that local algebras of a Jordan algebra inherit nondegeneracy, strong primeness, primitivity and semi-primitivity. Two main cases are to consider: algebras with a nonzero hermitian part, and PI algebras. Non PI strong prime Jordan algebras are first considered, then non PI primitive Jordan algebras, and finally PI primitive Jordan algebras. The main result is: Let \(J\) be a Jordan algebra, \(0\neq a\in J\). If \(J\) is nondegenerate, \(J_ a\) is nondegenerate. If \(J\) is primitive, \(J_ a\) is primitive. If \(J\) is strongly prime, \(J_ a\) is strongly prime. If \(J\) is semiprimitive, \(J_ a\) is semiprimitive.
Mathematics Subject Classification ID: 17C10
zbMATH DE Number: 769518
zbMATH Keywords: local algebras
zbMATH Keywords: Jordan algebra
zbMATH Keywords: nondegeneracy
zbMATH Keywords: strong primeness
zbMATH Keywords: primitivity
zbMATH Keywords: semi-primitivity
zbMATH Keywords: PI algebras
reviewed by: Monique Bertrand
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 769518