Planar, infinite, semidistributive lattices
Rings and Algebras
2023-09-26 v3
Abstract
An FN lattice is a simple, infinite, semidistributive lattice. Its existence was recently proved by R. Freese and J.\,B. Nation. Let denote the Boolean lattice with atoms. For a lattice , let denote with a new unit adjoined. We prove that the finite distributive lattices: can be represented as congruence lattices of infinite semidistributive lattices. The case is the Freese-Nation result, which is utilized in the proof. We also prove some related representation theorems.
Keywords
Cite
@article{arxiv.2306.04113,
title = {Planar, infinite, semidistributive lattices},
author = {George Grätzer and J. B. Nation},
journal= {arXiv preprint arXiv:2306.04113},
year = {2023}
}