On the socle of a Jordan pair
type: Item
instance of: scholarly article
title: On the socle of a Jordan pair
zbMATH Open document ID: 0729.17022
author: Ottmar Loos
published in: Collectanea Mathematica
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/39407
review text: The author studies the socle Soc V\(=(Soc V^+,Soc V^-)\) of a Jordan pair \(V=(V^+,V^-)\) where Soc \(V^{\sigma}\) is the sum of all inner ideals of \(V^{\sigma}\) that are simple or trivial. For nondegenerate V he characterizes the elements of Soc \(V^+\) by showing \(u\in Soc V^+\) if and only if the inner ideal generated by u has dcc on principal inner ideals. The socle is shown to be a direct sum of simple ideals. Moreover, the socle allows a description as direct limit of subpairs of finite capacity.
Mathematics Subject Classification ID: 17C20
Mathematics Subject Classification ID: 17C10
zbMATH DE Number: 4204626
zbMATH Keywords: socle
zbMATH Keywords: Jordan pair
zbMATH Keywords: inner ideals
reviewed by: Armin Thedy
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4204626