Towards a Goldie theory for Jordan pairs
type: Item
instance of: scholarly article
title: Towards a Goldie theory for Jordan pairs
zbMATH Open document ID: 0898.17013
DOI: 10.1007/BF02678016
author: Antonio Fernández López
author: E. García Rus
author: Omar Jaa
published in: Manuscripta Mathematica
publication date: 1998-11-03T00:00:00Z
review text: The paper under review is devoted to start a Goldie theory for linear Jordan pairs. To do this, a notion of order is defined and it is shown the compatibility with the previous concept of order in Jordan algebras, introduced by \textit{E. I. Zelmanov} [Sib. Math. J. 28, 899-906 (1987); translation from Sib. Mat. Zh. 28, No. 6, 44-52 (1987; 638.17012) and Sib. Math. J. 29, 567-573 (1988); translation from Sib. Mat. Zh. 29, No. 4, 68-74 (1988; Zbl 0663.17016)]. The main result asserts that a linear Jordan pair \(V\) which is an order in a nondegenerate and locally artinian linear Jordan pair \(W\) is nondegenerate, satisfies the ascending chain condition on annihilators of elements and has finite Goldie dimension. Moreover, \(V\) is strongly prime if and only if \(W\) is simple.
reviewed by: Alberto Elduque
Mathematics Subject Classification ID: 17C10
zbMATH DE Number: 1135226
zbMATH Keywords: Goldie theory
zbMATH Keywords: Jordan pair
zbMATH Keywords: local algebra
zbMATH Keywords: annihilator
zbMATH Keywords: chain condition
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02678016
OpenAlex ID: W2076832660
description: scientific article; zbMATH DE number 1135226