Multipasting of lattices
type: Item
instance of: scholarly article
title: Multipasting of lattices
zbMATH Open document ID: 0787.06006
DOI: 10.1007/BF01196095
published in: Algebra Universalis
publication date: 1994-05-19T00:00:00Z
review text: A new lattice construction called multipasting is introduced; this generalizes the constructions of gluing, pasting and \(S\)-glued sum, which were investigated in several papers. A multipasting of a family of lattices \(L_ \lambda\) \((\lambda\in\Lambda)\) is a lattice \(L\) such that all \(L_ \lambda\) are sublattices of \(L\) satisfying certain conditions (the detailed definition would be too lengthy to be reproduced here). By using the notion of \(\Sigma\)-pasting it is proved that multipasting can be in fact treated as a construction, thus the family \(L_ \lambda\) \((\lambda\in\Lambda)\) of lattices can be arbitrary. The relations between multipasting and the above-mentioned types of constructions are studied. Next, by applying stronger sets of conditions, the authors define and investigate the notions of (i) strong multipasting, (ii) multipasting of convex sublattices, and (iii) multipasting with the (upper) interpolation property. The results on strong multipasting concern lattices of finite length. Some open problems are proposed.
Mathematics Subject Classification ID: 06B05
zbMATH DE Number: 203152
zbMATH Keywords: multipasting
zbMATH Keywords: gluing
zbMATH Keywords: pasting
zbMATH Keywords: \(S\)-glued sum
zbMATH Keywords: strong multipasting
zbMATH Keywords: convex sublattices
zbMATH Keywords: interpolation property
zbMATH Keywords: lattices of finite length
author: Ervin Fried
author: G. Grätzer
author: E. T. Schmidt
reviewed by: Ján Jakubík
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01196095
OpenAlex ID: W2080645404
description: scientific article; zbMATH DE number 203152