ACTA issues

On the number of atoms in three-generated lattices

Gábor Czédli

Acta Sci. Math. (Szeged) 87:1-2(2021), 3-18

Abstract. 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.

DOI: 10.14232/actasm-020-769-4

AMS Subject Classification (1991): 06B99

Keyword(s): three-generated lattice, number of atoms, coatom, atomless lattice, herringbone lattice, $n$-distributive lattice, 2-distributive lattice, non-finitely presented lattice, convex geometry, meet-distributive lattice, semidistributive lattice, semimodular lattice

received 9.1.2020, revised 8.10.2020, accepted 4.12.2020. (Registered under 19/2020.)