- Tytuł:
- Congruences and Trajectories in Planar Semimodular Lattices
- Autorzy:
- Grätzer, G.
- Powiązania:
- https://bibliotekanauki.pl/articles/52488033.pdf
- Data publikacji:
- 2018-06-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
semimodular lattice
planar lattice
slim lattice
rectangular lattice
congruence
trajectory
prime interval - Opis:
- A 1955 result of J. Jakubík states that for the prime intervals \(\mathfrak{p}\) and \(\mathfrak{q}\) of a finite lattice, \(con(\mathfrak{p}) ≥ con(\mathfrak{q})\) iff \(\mathfrak{p}\) is congruence-projective to \(\mathfrak{q}\) (via intervals of arbitrary size). The problem is how to determine whether \(con(\mathfrak{p}) ≥ con(\mathfrak{q})\) involving only prime intervals. Two recent papers approached this problem in different ways. G. Czédli’s used trajectories for slim rectangular lattices-a special subclass of slim, planar, semimodular lattices. I used the concept of prime-projectivity for arbitrary finite lattices. In this note I show how my approach can be used to reprove Czédli’s result and generalize it to arbitrary slim, planar, semimodular lattices.
- Źródło:
-
Discussiones Mathematicae - General Algebra and Applications; 2018, 38, 1; 131-142
1509-9415 - Pojawia się w:
- Discussiones Mathematicae - General Algebra and Applications
- Dostawca treści:
- Biblioteka Nauki
Artykuł