G. Gratzer

activity

20132023

most citedThe order of principal congruences of a semimodular lattice

1 citations · 1 across the 10 of their papers we have counts for

collaborators

10 papers

math.RA2023

Planar, infinite, semidistributive lattices

George Grätzer, J. B. Nation

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 w…

math.RA2023

An open problem on congruences of finite lattices

George Grätzer

Let $L$ be a planar semimodular lattice. We call $L$ \emph{slim}, if it has no $\mthree$ sublattice. Let us define an \emph{SPS lattice} as a slim, planar, semimodular lattice $L$ .…

math.RA2021

Using the Swing Lemma and $C_{1}$ -diagrams for congruences of planar semimodular lattices

George Grätzer

A planar semimodular lattice $K$ is \emph{slim} if $M_{3}$ is not a sublattice of~ $K$ . In a recent paper, G. Czédli found four new properties of congruence lattices of sli…

math.RA2021

Characterizing representability by principal congruences for finite distributive lattices with a join-irreducible unit element

George Grätzer

For a finite distributive lattice $D$ , let us call $Q \subseteq D$ \emph{principal congruence representable}, if there is a finite lattice $L$ such that the congruence lattice of $…

math.RA2021

Applying the Czédli-Schmidt Sequences to congruence properties of planar semimodular lattices

G. Grätzer

Following G.~Grätzer and E.~Knapp, 2009, a planar semimodular lattice $L$ is \emph{rectangular}, if~the left boundary chain has exactly one doubly-irreducible element, $c_{l}$ , and t…

math.RA2021

Atom-generated planar lattices

G. Grätzer

In this note, we discuss planar lattices generated by their atoms. We prove that if $L$ is a planar lattice generated by $n$ atoms, then both the left and the right boundaries of $…

math.RA2021

Using the Swing Lemma and Czédli diagrams for congruences of planar semimodular lattices

George Grätzer

A planar semimodular lattice $K$ is \emph{slim} if $M_{3}$ is not a sublattice of~ $K$ . In a recent paper, G. Czédli found four new properties of congruence lattices of slim,…

math.CO2021

Notes on planar semimodular lattices. IX. $C_{1}$ -diagrams

George Grätzer

A planar semimodular lattice $L$ is \emph{slim} if $M_{3}$ is not a sublattice of $L$ . In a recent paper, G. Czédli introduced a very powerful diagram type for slim, planar,…

math.RA2013★ 1 cited

The order of principal congruences of a semimodular lattice

G. Grätzer, E. T. Schmidt

This paper has been withdrawn by the authors due to a crucial computational error. In this paper we deal with the finite case. We prove that a finite bounded ordered set can be rep…

math.RA2013

The order of principal congruences of a bounded lattice

G. Grätzer

We characterize the order of principal congruences of a bounded lattice (also of a complete lattice and of a lattice of length 5) as a bounded ordered set. We also state a number o…

Planar, infinite, semidistributive lattices

An open problem on congruences of finite lattices

Using the Swing Lemma and C1​-diagrams for congruences of planar semimodular lattices

Characterizing representability by principal congruences for finite distributive lattices with a join-irreducible unit element

Applying the Czédli-Schmidt Sequences to congruence properties of planar semimodular lattices

Atom-generated planar lattices

Using the Swing Lemma and Czédli diagrams for congruences of planar semimodular lattices

Notes on planar semimodular lattices. IX. C1​-diagrams

The order of principal congruences of a semimodular lattice

The order of principal congruences of a bounded lattice

Using the Swing Lemma and $C_{1}$ -diagrams for congruences of planar semimodular lattices

Notes on planar semimodular lattices. IX. $C_{1}$ -diagrams