Mathematica Bohemica, Vol. 148, No. 1, pp. 95-104, 2023
Meet-distributive lattices have the intersection property
Henri Mühle
Received May 17, 2021. Published online April 28, 2022.
Abstract: This paper is an erratum of H. Mühle: Distributive lattices have the intersection property, Math. Bohem. (2021). Meet-distributive lattices form an intriguing class of lattices, because they are precisely the lattices obtainable from a closure operator with the so-called anti-exchange property. Moreover, meet-distributive lattices are join semidistributive. Therefore, they admit two natural secondary structures: the core label order is an alternative order on the lattice elements and the canonical join complex is the flag simplicial complex on the canonical join representations. In this article we present a characterization of finite meet-distributive lattices in terms of the core label order and the canonical join complex, and we show that the core label order of a finite meet-distributive lattice is always a meet-semilattice.
Affiliations: Henri Mühle, Technische Universität Dresden, Institut für Algebra, Zellescher Weg 12-14, 01069 Dresden, Germany, e-mail: henri.muehle@tu-dresden.de