Small non-Arguesian lattices
type: Item
instance of: scholarly article
title: Small non-Arguesian lattices
zbMATH Open document ID: 0808.06007
DOI: 10.1007/BF01188180
author: Alan Day
author: Christian Herrmann
author: Bjarni Jónsson
author: J. B. Nation
author: Doug Pickering
published in: Algebra Universalis
publication date: 1994-04-07T00:00:00Z
review text: The authors study how for small skeletons the gluing structure of a modular lattice is related to the Arguesian identity and representability in lattices of submodules resp. permuting equivalences. In particular, each Arguesian lattice of length \(\leq 5\) is shown to have such a representation -- for length 8, there are counterexamples due to Haiman.
reviewed by: Christian Herrmann
Mathematics Subject Classification ID: 06C05
zbMATH DE Number: 513020
zbMATH Keywords: small skeletons
zbMATH Keywords: gluing structure
zbMATH Keywords: modular lattice
zbMATH Keywords: representability in lattices of submodules
zbMATH Keywords: permuting equivalences
zbMATH Keywords: Arguesian lattice
MaRDI profile type: Publication
cites work: Inducing lattice maps by semilinear isomorphisms
cites work: Gluings of modular lattices
cites work: The structure of non-Arguesian lattices
cites work: A structural characterization of non-Arguesian lattices
cites work: Q3803171
cites work: Non-Arguesian configurations and gluings of modular lattices
cites work: The Variety of Modular Lattices is Not Generated by its Finite Members
cites work: Q4149775
cites work: Two notes on the Arguesian identity
cites work: Arguesian lattices which are not type-1
cites work: The imbedding problem for modular lattices
cites work: S-verklebte Summen von Verbänden
cites work: Quasiplanare Verbände
cites work: A geometric description of modular lattices
cites work: Q5829441
cites work: Arguesian Lattices of Dimension $n\leqq 4$.
cites work: The class of Arguesian lattices is self-dual
cites work: Arguesian lattices whose skeleton is a chain
cites work: Q5557964
cites work: Q4724676
full work available at URL: https://doi.org/10.1007/bf01188180
OpenAlex ID: W2054311617
description: scientific article; zbMATH DE number 513020