Displaying similar documents to “Completely meet-irreducible tolerances in distributive Noetherian lattices”

Going down in (semi)lattices of finite Moore families and convex geometries

Bordalo Gabriela, Caspard Nathalie, Monjardet Bernard (2009)

Czechoslovak Mathematical Journal

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In this paper we first study what changes occur in the posets of irreducible elements when one goes from an arbitrary Moore family (respectively, a convex geometry) to one of its lower covers in the lattice of all Moore families (respectively, in the semilattice of all convex geometries) defined on a finite set. Then we study the set of all convex geometries which have the same poset of join-irreducible elements. We show that this set—ordered by set inclusion—is a ranked join-semilattice...