An open problem on congruences of finite lattices

2023/03/01 by Grätzer, George
#06 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2303.00699

Abstract

Let L be a planar semimodular lattice. We call L slim, if it has no \mthree sublattice. Let us define an SPS lattice as a slim, planar, semimodular lattice L. 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 Gábor Czédli.

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