LE LATTIS DES SOUS-ALGÈBRES D'UNE ALGÈBRE DE HEYTING FINIE
L. VRANCKEN-MAWET,
Université de Liège, Institut de Mathématique, 15 avenue des Tilleuls, 4000 Liège, Belgique.
Abstract
In this paper, we investigate the subalgebra lattice of a finite Heyting algebra. Among other things, we prove that this lattice is always lower semimodular. We also characterize those finite Heyting algebras whose subalgebra lattice is distributive, dually atomistic or Boolean. Finally, we prove that a finite Heyting algebra is isomorphic with the Frattini subalgebra of some finite Heyting algebra if and only if it contains a least A-irreducible element. To achieve these results, we adapt to the finite Heyting algebras the well-known duality between finite distributive lattices and finite posets.
Pour citer cet article
L. VRANCKEN-MAWET, «LE LATTIS DES SOUS-ALGÈBRES D'UNE ALGÈBRE DE HEYTING FINIE», Bulletin de la Société Royale des Sciences de Liège [En ligne], Volume 51 - Année 1982, Numéro 1 - 2, 82 - 94 URL : https://popups.uliege.be/0037-9565/index.php?id=1354.