Laterally closed lattice homomorphisms
type: Item
instance of: scholarly article
title: Laterally closed lattice homomorphisms
zbMATH Open document ID: 1115.06010
author: Nedra Toumi
author: Mohamed Ali Toumi
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-11-15T00:00:00Z
review text: A lattice homomorphism \(T: A\to B\) between two Archimedean vector lattices is called laterally closed if \(T(D)\) is a maximal orthogonal system in the band generated by \(T(A)\subset B\) for each maximal orthogonal system \(D\subset A\). The authors prove that any laterally closed \(T\) into a universally complete vector lattice \(B\) can be extended to a lattice homomorphism of the universal completion \(A^u\) into \(B\). This is an improvement of a result of \textit{M. Duhoux} and \textit{M. Meyer} [Ann. Soc. Sci. Bruxelles, Sér. I 98, 3--18 (1984; Zbl 0559.46003)].
Mathematics Subject Classification ID: 06F20
Mathematics Subject Classification ID: 06F25
Mathematics Subject Classification ID: 46A40
zbMATH DE Number: 5073015
zbMATH Keywords: laterally closed lattice homomorphism
zbMATH Keywords: \(d\)-algebra
zbMATH Keywords: \(f\)-algebra
reviewed by: Beloslav Riečan
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.01.019
OpenAlex ID: W1973937881
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DOI: 10.1016/J.JMAA.2006.01.019
description: scientific article; zbMATH DE number 5073015