Congruence amalgamation of lattices - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Acta Sci. Math. (Szeged) Année : 2000

Congruence amalgamation of lattices

Résumé

J. Tuma proved an interesting "congruence amalgamation" result. We are generalizing and providing an alternate proof for it. We then provide applications of this result: ---A.P. Huhn proved that every distributive algebraic lattice $D$ with at most $\aleph_1$ compact elements can be represented as the congruence lattice of a lattice $L$. We show that $L$ can be constructed as a locally finite relatively complemented lattice with zero. ---We find a large class of lattices, the $\omega$-congruence-finite lattices, that contains all locally finite countable lattices, in which every lattice has a relatively complemented congruence-preserving extension.
Fichier principal
Vignette du fichier
CongAmal.pdf (165.93 Ko) Télécharger le fichier
Loading...

Dates et versions

hal-00004029 , version 1 (22-01-2005)

Identifiants

Citer

George Grätzer, Harry Lakser, Friedrich Wehrung. Congruence amalgamation of lattices. Acta Sci. Math. (Szeged), 2000, 66, pp.339-358. ⟨hal-00004029⟩
48 Consultations
59 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More