Minimal representations of a finite distributive lattice by principal\n congruences of a lattice

2021/04/29 by George Grätzer, Grätzer, G., H. Lakser +1
Computer Science · Decision Sciences · #06B10 #Advanced Algebra and Logic #FOS: Mathematics #Multi-Criteria Decision Making #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.2104.14693

openalex publication_date 2021/04/29 · openalex created_date 2021/05/10 · openalex updated_date 2026/08/04

Abstract

Let the finite distributive lattice D be isomorphic to the congruence\nlattice of a finite lattice L. Let Q denote those elements of D that\ncorrespond to principal congruences under this isomorphism. Then Q contains\n0,1 \∈ D and all the join-irreducible elements of D. If Q contains\nexactly these elements, we say that L is a minimal representations of D by\nprincipal congruences of the lattice L.\n We characterize finite distributive lattices D with a minimal\nrepresentation by principal congruences with the property that D has at most\ntwo dual atoms.\n

Citations

• Homomorphisms and principal congruences of bounded lattices

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