On the number of atoms in three-generated lattices

As the main result of the paper, we construct a three-generated, 2- distributive, atomless lattice that is not finitely presented. Also, the paper contains the following three observations. First, every coatomless three-generated lattice has at least one atom. Second, we give some sufficient conditi...

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Bibliographic Details
Main Author: Czédli Gábor
Format: Article
Published: 2021
Series:Acta scientiarum mathematicarum 87 No. 1-2
Kulcsszavak:Matematika
doi:10.14232/actasm-020-769-4

Online Access:http://acta.bibl.u-szeged.hu/73915
Description
Summary:As the main result of the paper, we construct a three-generated, 2- distributive, atomless lattice that is not finitely presented. Also, the paper contains the following three observations. First, every coatomless three-generated lattice has at least one atom. Second, we give some sufficient conditions implying that a three-generated lattice has at most three atoms. Third, we present a three-generated meet-distributive lattice with four atoms.
Physical Description:23-38
ISSN:2064-8316