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.)
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