Dedekind's numbers characterize distributive lattices
type: Item
instance of: scholarly article
title: Dedekind's numbers characterize distributive lattices
zbMATH Open document ID: 0723.06010
DOI: 10.1007/BF01190409
published in: Algebra Universalis
publication date: 1991-01-01T00:00:00Z
review text: The main result is as follows. Let D(n) denote the cardinality of the free bounded distributive lattice on n free generators. A nontrivial algebra is equivalent to a distributive lattice if and only if the number of n-ary polynomials over the algebra is equal to D(n)-2, for all \(n\geq 0.\) The representability rank and the code of the variety of distributive lattices are presented.
Mathematics Subject Classification ID: 06D05
Mathematics Subject Classification ID: 08A40
zbMATH DE Number: 4191758
zbMATH Keywords: number of polynomials
zbMATH Keywords: representability rank
zbMATH Keywords: code of the variety of distributive lattices
author: Józef Dudek
reviewed by: Josef Niederle
MaRDI profile type: Publication
cites work: Q3739184
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full work available at URL: https://doi.org/10.1007/bf01190409
OpenAlex ID: W2029947894
description: scientific article; zbMATH DE number 4191758