Mathematica Bohemica, first online, pp. 1-10


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.
Keywords:  meet-distributive lattice; congruence-uniform lattice; canonical join complex; core label order; intersection property
Classification MSC:  06D75
DOI:  10.21136/MB.2022.0072-21

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Affiliations:   Henri Mühle, Technische Universität Dresden, Institut für Algebra, Zellescher Weg 12-14, 01069 Dresden, Germany, e-mail: henri.muehle@tu-dresden.de


 
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