Kyungpook Mathematical Journal 2020; 60(1): 1-20
Published online March 31, 2020
Copyright © Kyungpook Mathematical Journal.
On the Representations of Finite Distributive Lattices
Department of Mathematics, Kyungpook National University, Daegu 41566, Republic of Korea
e-mail : firstname.lastname@example.org
Received: January 24, 2017; Revised: January 16, 2020; Accepted: January 16, 2020
A simple but elegant result of Rival states that every sublattice
Applying this in the case that ℘ is a product of a finite set of chains, we get a one-to-one correspondence between the sublattices of ℘ and the preorders spanned by a canonical sublattice of ℘.
We then show that
With this we recover and extend, among other classical results, the correspondence derived from results of Birkhoff and Dilworth, between the tight embeddings of a finite distributive lattice
Keywords: finite distributive lattice, representation, embedding, product of chains.