2021/04/27 by George Grätzer, Grätzer, George
Computer Science · #06C10 #Advanced Algebra and Logic #FOS: Mathematics #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2104.13444
openalex publication_date 2021/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A planar semimodular lattice K is slim if M3 is not a sublattice of~K. In a recent paper, G. Czédli found four new properties of congruence lattices of slim, planar, semimodular lattices, including the No Child Property: Let~P be the ordered set of join-irreducible congruences of K. Let x,y,z ∈ P and let z be a~maximal element of P. If x ≠ y, x, y \prec z in P, then there is no element u of P such that u \prec x, y in P. We are applying my Swing Lemma, 2015, and a type of standardized diagrams of Czédli's, to verify Czédli's four properties.