Distributive lattices have the intersection property

Henri Mühle

Mathematica Bohemica (2021)

  • Issue: 1, page 7-17
  • ISSN: 0862-7959

Abstract

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Distributive lattices form an important, well-behaved class of lattices. They are instances of two larger classes of lattices: congruence-uniform and semidistributive lattices. Congruence-uniform lattices allow for a remarkable second order of their elements: the core label order; semidistributive lattices naturally possess an associated flag simplicial complex: the canonical join complex. In this article we present a characterization of finite 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 distributive lattice is always a meet-semilattice.

How to cite

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Mühle, Henri. "Distributive lattices have the intersection property." Mathematica Bohemica (2021): 7-17. <http://eudml.org/doc/297084>.

@article{Mühle2021,
abstract = {Distributive lattices form an important, well-behaved class of lattices. They are instances of two larger classes of lattices: congruence-uniform and semidistributive lattices. Congruence-uniform lattices allow for a remarkable second order of their elements: the core label order; semidistributive lattices naturally possess an associated flag simplicial complex: the canonical join complex. In this article we present a characterization of finite 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 distributive lattice is always a meet-semilattice.},
author = {Mühle, Henri},
journal = {Mathematica Bohemica},
keywords = {distributive lattice; congruence-uniform lattice; canonical join complex; core label order; intersection property},
language = {eng},
number = {1},
pages = {7-17},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Distributive lattices have the intersection property},
url = {http://eudml.org/doc/297084},
year = {2021},
}

TY - JOUR
AU - Mühle, Henri
TI - Distributive lattices have the intersection property
JO - Mathematica Bohemica
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 7
EP - 17
AB - Distributive lattices form an important, well-behaved class of lattices. They are instances of two larger classes of lattices: congruence-uniform and semidistributive lattices. Congruence-uniform lattices allow for a remarkable second order of their elements: the core label order; semidistributive lattices naturally possess an associated flag simplicial complex: the canonical join complex. In this article we present a characterization of finite 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 distributive lattice is always a meet-semilattice.
LA - eng
KW - distributive lattice; congruence-uniform lattice; canonical join complex; core label order; intersection property
UR - http://eudml.org/doc/297084
ER -

References

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