A note on finite lattices with many congruences

2017/12/17 by Gábor Czédli, Czédli, Gábor · 2 citations
Computer Science · #06B10 #Advanced Algebra and Logic #FOS: Mathematics #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1712.06117

openalex publication_date 2017/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By a twenty year old result of Ralph Freese, an n-element lattice L has at most 2^n-1 congruences. We prove that if L has less than 2^n-1 congruences, then it has at most 2^n-2 congruences. Also, we describe the n-element lattices with exactly 2^n-2 congruences.

Cited by

• Some Extremal Values of the Number of Congruences of a Finite Lattice
• A Note on Congruences of Infinite Bounded Involution Lattices

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