Les ensembles partiellement ordonnés et le théorème de raffinement de Schreier. II. Théorie des multistructures
Les préordres totaux compatibles avec un ordre partiel
Les sous-groupes d'un groupe quasi-réticulé
Les termes : un modèle algébrique de représentation et de structuration de données symboliques
Nos travaux se situent dans le cadre de l'analyse conceptuelle des données. Notre objectif est de généraliser les représentations par variables binaires ou nominales en y adjoignant la modélisation de structures internes. Le problème est de ne pas perdre en complexité algorithmique ce qui est gagné en puissance de représentation. Selon ces considérations, décrire les données et des classes de données par des structures arborescentes semble un bon compromis. Le système de représentation que nous...
L'Espace Vectoriel Pseudo-Booléen Généralisé
Lexico extension and a cut completion of a half l-group
The cut completi on of an hl-group G with the abelian increasing part is investigated under the assumption that G is a lexico extension of its hl-subgroup.
Lexicographic extensions of dually residuated lattice ordered monoids
Dually residuated lattice ordered monoids (-monoids) are common generalizations of, e.g., lattice ordered groups, Brouwerian algebras and algebras of logics behind fuzzy reasonings (-algebras, -algebras) and their non-commutative variants (-algebras, pseudo -algebras). In the paper, lex-extensions and lex-ideals of -monoids (which need not be commutative or bounded) satisfying a certain natural condition are studied.
Lexicographic factors of a linearly ordered group
Lexicographic product decompositions of a linearly ordered group
Lexicographic product decompositions of cyclically ordered groups
Lexicographic product decompositions of half linearly ordered loops
In this paper we prove for an hl-loop an assertion analogous to the result of Jakubík concerning lexicographic products of half linearly ordered groups. We found conditions under which any two lexicographic product decompositions of an hl-loop with a finite number of lexicographic factors have isomorphic refinements.
Lexicographic product decompositions of partially ordered quasigroups
Lexicographic products of cyclically ordered groups
Lexicographic products of half linearly ordered groups
The notion of the half linearly ordered group (and, more generally, of the half lattice ordered group) was introduced by Giraudet and Lucas [2]. In the present paper we define the lexicographic product of half linearly ordered groups. This definition includes as a particular case the lexicographic product of linearly ordered groups. We investigate the problem of the existence of isomorphic refinements of two lexicographic product decompositions of a half linearly ordered group. The analogous problem...
Lex-ideals of DR-monoids and GMV-algebras
Liaisons entre les S-relations et les relations de ferrers. Représentations
Limits of families of measure algebras
Linear Congruences in Distributive Lattices
Linear extensions of orderings
A construction is given which makes it possible to find all linear extensions of a given ordered set and, conversely, to find all orderings on a given set with a prescribed linear extension. Further, dense subsets of ordered sets are studied and a procedure is presented which extends a linear extension constructed on a dense subset to the whole set.
Linear extensions of orders invariant under abelian group actions
Let G be an abelian group acting on a set X, and suppose that no element of G has any finite orbit of size greater than one. We show that every partial order on X invariant under G extends to a linear order on X also invariant under G. We then discuss extensions to linear preorders when the orbit condition is not met, and show that for any abelian group acting on a set X, there is a linear preorder ≤ on the powerset 𝓟X invariant under G and such that if A is a proper subset of B, then A < B...