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 conditio...

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Bibliographic Details
Published in:Acta scientiarum mathematicarum (Szeged) 2021-01, Vol.87 (1-2), p.23-38
Main Author: Czédli, Gábor
Format: Article
Language:English
Subjects:
Algebra
Functional Analysis
Mathematics
Operator Theory
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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.
ISSN:0001-6969
2064-8316
DOI:10.14232/actasm-020-769-4