An elemental characterization of strong primeness in Jordan systems
type: Item
instance of: scholarly article
title: An elemental characterization of strong primeness in Jordan systems
zbMATH Open document ID: 0967.17021
DOI: 10.1016/0022-4049(95)00086-0
author: Teresa Cortés
author: Ottmar Loos
author: José A. Anquela
author: Kevin McCrimmon
published in: Journal of Pure and Applied Algebra
publication date: 2001-07-18T00:00:00Z
review text: The authors give elemental characterizations of strong primeness for Jordan algebras, pairs and triple systems. Using \textit{K. McCrimmon}'s approach [Algebras Groups Geom. 1, 217-234 (1984; Zbl 0562.17006)] they prove that a Jordan pair \(V= (V^+, V^-)\) is strongly prime if and only if for all \(\sigma= \pm\) and \(a,b\in V^\sigma\), \(Q_a Q_b (V^\sigma) Q_b= 0\) implies \(a=0\) or \(b=0\). For a Jordan triple system an analogous condition for strong primeness is given. They use their characterization to study the transfer of strong primeness between a Jordan system and its local algebras and subquotients.
Mathematics Subject Classification ID: 17C10
zbMATH DE Number: 896547
zbMATH Keywords: strong primeness
zbMATH Keywords: Jordan algebras
zbMATH Keywords: Jordan pair
zbMATH Keywords: Jordan triple system
MaRDI profile type: Publication
full work available at URL: 0022-4049(95)00086-0
OpenAlex ID: W2020880625
Wikidata QID: Q115130072
cites work: Local inheritance in Jordan algebras
cites work: Q3792852
cites work: Quadratic Jordan systems of Hermitian type
cites work: The local algebras of Jordan systems
cites work: Q3953947
cites work: Jordan pairs
cites work: On the socle of a Jordan pair
cites work: Complementation of inner ideals in Jordan pairs
cites work: Peirce ideals in Jordan triple systems
cites work: Q5187431
cites work: Q3781902
description: scientific article; zbMATH DE number 896547