Über Mengen mit Trennrelationen
We define an ultra -ideal of a lattice implication algebra and give equivalent conditions for an -ideal to be ultra. We show that every subset of a lattice implication algebra which has the finite additive property can be extended to an ultra -ideal.
A mistake concerning the ultra -ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an -ideal to be an ultra -ideal are given. Moreover, the notion of an -ideal is extended to -algebras, the notions of a (prime, ultra, obstinate, Boolean) -ideal and an -ideal of an -algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in -algebra: (1) prime proper -ideal and Boolean -ideal,...
Cette étude s'inscrit dans un prolongement algorithmique d'un travail de Bruno Leclerc, publié dans cette revue, qui discute de la taille maximum d'une antichaîne dans un produit direct P d'ordres totaux. On y présente un algorithme de partitionnement de P en un nombre minimum de chaînes. Enfin, on décrit brièvement une application à l'extraction de connaissance.