Isoform lattices

2013/09/29 by G. Grätzer, George Grätzer, E. T. Schmidt +5
Computer Science · Mathematics · #06B10 #06B15 #Advanced Algebra and Logic #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:06B10 #msc:06B15

paper · pdf · doi:10.48550/arxiv.1309.7525

arxiv created 2013/09/29 · openalex publication_date 2013/09/29 · arxiv updated 2013/10/01 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

Let L be a lattice. We call a congruence relation \gQ of L isoform, if any two congruence classes of \gQ are isomorphic (as lattices). Let us call the lattice L isoform, if all congruences of L are isoform. G. Grätzer and E. T. Schmidt proved that every finite distributive lattice D can be represented as the congruence lattice of a finite isoform lattice L. We now prove that every finite lattice K has a congruence-preserving extension to a finite isoform lattice L.

Related

• Representing finite distributive lattices as congruence lattices of lattices
• Some preliminary results on the set of principal congruences of a finite lattice
• 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
• A short proof of the congruence representation theorem for semimodular lattices