G. Gratzer

most citedThe order of principal congruences of a semimodular lattice

1 citations · 1 across the 3 of their papers we have counts for

collaborators

8 papers

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,…

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

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

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