Bulletin de la Société Royale des Sciences de Liège

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L. VRANCKEN-MAWET

LE LATTIS DES SOUS-ALGÈBRES D'UNE ALGÈBRE DE HEYTING FINIE

(Volume 51 - Année 1982 — Numéro 1 - 2)
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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.

To cite this 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.

About:  L. VRANCKEN-MAWET

Université de Liège, Institut de Mathématique, 15 avenue des Tilleuls, 4000 Liège, Belgique.