Atom-generated planar lattices

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 L have at most n + 1 elements. On the other hand, L can be arbitrarily large. For every k > 1, we construct a planar latti...

Teljes leírás

Elmentve itt :
Bibliográfiai részletek
Szerző: Grätzer G.
Dokumentumtípus: Cikk
Megjelent: 2020
Sorozat:Acta scientiarum mathematicarum 86 No. 3-4
Kulcsszavak:Algebra, Matematika
doi:10.14232/actasm-020-363-7

Online Access:http://acta.bibl.u-szeged.hu/73895
Leíró adatok
Tartalmi kivonat: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 L have at most n + 1 elements. On the other hand, L can be arbitrarily large. For every k > 1, we construct a planar lattice L generated by 4 atoms such that L has more than k elements.
Terjedelem/Fizikai jellemzők:351-357
ISSN:2064-8316