2015/07/12 by George Grätzer, Grätzer, George · 2 citations
Computer Science · Decision Sciences · Mathematics · #06B10 #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic #math.RA #msc:06B10
paper · pdf · doi:10.48550/arxiv.1507.03270
openalex publication_date 2015/07/12 · arxiv created 2015/08/16 · arxiv updated 2015/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Two years ago, I characterized the order \Princl L of principal congruences of a bounded lattice L as a bounded order. If K and L are bounded lattices and \gf is a \zo homomorphism of K into~L, then there is a natural isotone \zo-map \gf\Hom from \Princl K into \Princl L. We prove the converse: For bounded orders P and Q and an isotone \zo map \gy of P into Q, we represent P and Q as \Princl K and \Princl L for bounded lattices K and L with a \zo homomorphism \gf of K into L, so that \gy is represented as \gf\Hom.