Representing finite distributive lattices as congruence lattices of lattices

2013/09/28 by George Grätzer, Grätzer, George
Mathematics · #06B10 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:06B10

paper · pdf · doi:10.48550/arxiv.1309.7511

arxiv created 2013/09/28 · arxiv updated 2013/10/01

Abstract

Dilworth's theorem. Every finite distributive lattice D can be represented as the congruence lattice of a finite lattice L. We want: Every finite distributive lattice D can be represented as the congruence lattice of a nice finite lattice L. nice = sectionally complemented, uniform, semimodular, given automorphism group, regular, uniform, isoform

Related

• Revisiting the representation theorem of finite distributive lattices with principal congruences
• A short proof of the congruence representation theorem for semimodular lattices
• The Congruences of a Finite Lattice, A "Proof-by-Picture" Approach, third edition
• Characterizing representability by principal congruences for finite\n distributive lattices with a join-irreducible unit element
• Isoform lattices