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LE LATTIS DES SOUS-ALGÈBRES D'UNE ALGÈBRE DE HEYTING FINIE
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.
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A propos de : L. VRANCKEN-MAWET
Université de Liège, Institut de Mathématique, 15 avenue des Tilleuls, 4000 Liège, Belgique.