English

An open problem on congruences of finite lattices

Rings and Algebras 2023-03-02 v1

Abstract

Let LL be a planar semimodular lattice. We call LL \emph{slim}, if it has no \mthree\mthree sublattice. Let us define an \emph{SPS lattice} as a slim, planar, semimodular lattice LL. In 2016, I proved a property of congruences of SPS lattices (Two-cover Property) and raised the problem of characterizing them. Since then, more than 50 papers have been published contributing to this problem. In this survey, I provide an overview of this field with major contributions by G\'abor Cz\'edli.

Keywords

Cite

@article{arxiv.2303.00699,
  title  = {An open problem on congruences of finite lattices},
  author = {George Grätzer},
  journal= {arXiv preprint arXiv:2303.00699},
  year   = {2023}
}