Stable \(f\)-algebras
type: Item
instance of: scholarly article
title: Stable \(f\)-algebras
zbMATH Open document ID: 1013.06021
author: Abdelmajid Triki
published in: Algebra Universalis
publication date: 2003-04-23T00:00:00Z
review text: The paper under review deals with ideals (algebra ideals, regular ideals and order ideals) of Archimedean \(f\)-algebras. The author introduces the class of stable \(f\)-algebras and extends some results on Archimedean \(f\)-algebras with unit to Archimedean stable \(f\)-algebras. He gives necessary and sufficient conditions on Archimedean \(f\)-algebras to have the property that every algebra ideal is an order ideal and shows that every such \(f\)-algebra is stable. Analogous conditions are found for Archimedean \(f\)-algebras in which every regular algebra ideal is an order ideal. Furthermore, the paper contains representation theorems for stable \(f\)-algebras and \(f\)-algebras in which every algebra ideal is an order ideal.
Mathematics Subject Classification ID: 06F25
zbMATH DE Number: 1899951
zbMATH Keywords: \(f\)-algebra
zbMATH Keywords: \(l\)-ideal
zbMATH Keywords: orthomorphism
reviewed by: Jiří Rachůnek
MaRDI profile type: Publication
full work available at URL: s000120050171
OpenAlex ID: W2072551819
DOI: 10.1007/S000120050171
description: scientific article; zbMATH DE number 1899951