Planar, infinite, semidistributive lattices

2023/06/07 by Grätzer, George, Nation, J. B.
#06 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2306.04113

Abstract

An FN lattice F is a simple, infinite, semidistributive lattice. Its existence was recently proved by R. Freese and J. B. Nation. Let B_n denote the Boolean lattice with n atoms. For a lattice K, let K⁺ denote K with a new unit adjoined. We prove that the finite distributive lattices: B₀⁺, B₁⁺,B₂⁺, … can be represented as congruence lattices of infinite semidistributive lattices. The case n = 0 is the Freese-Nation result, which is utilized in the proof. We also prove some related representation theorems.

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