A Note on Congruences of Infinite Bounded Involution Lattices

2018/09/29 by Claudia Mureșan, Mureşan, Claudia
Computer Science · Decision Sciences · #06B10 #06D30 #06F99 #Advanced Algebra and Logic #Combinatorics (math.CO) #FOS: Mathematics #Fuzzy and Soft Set Theory #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.1810.00277

openalex publication_date 2018/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that an infinite (bounded) involution lattice and even pseudo--Kleene algebra can have any number of congruences between 2 and its number of elements or equalling its number of subsets, regardless of whether it has as many ideals as elements or as many ideals as subsets; consequently, the same holds for antiortholattices. Under the Generalized Continuum Hypothesis, this means that an infinite (bounded) involution lattice, pseudo--Kleene algebra or antiortholattice can have any number of congruences between 2 and its number of subsets, regardless of its number of ideals.

Citations

• A note on finite lattices with many congruences

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