Bounded countable atomic compactness of ordered groups
Bounded dually residuated lattice ordered monoids as a generalization of fuzzy structures
Certain partial orders on semigroups
Relations introduced by Conrad, Drazin, Hartwig, Mitsch and Nambooripad are discussed on general, regular, completely semisimple and completely regular semigroups. Special properties of these relations as well as possible coincidence of some of them are investigated in some detail. The properties considered are mainly those of being a partial order or compatibility with multiplication. Coincidences of some of these relations are studied mainly on regular and completely regular semigroups.
Characterizing ordered quasi-ideals of ordered -semigroups
Characterizing ordered semigroups by means of intuitionistic fuzzy bi-ideals.
Classes of filters in generalizations of commutative fuzzy structures
Bounded commutative residuated lattice ordered monoids (-monoids) are a common generalization of -algebras and Heyting algebras, i.e. algebras of basic fuzzy logic and intuitionistic logic, respectively. In the paper we develop the theory of filters of bounded commutative -monoids.
Classes of fuzzy filters of residuated lattice ordered monoids
The logical foundations of processes handling uncertainty in information use some classes of algebras as algebraic semantics. Bounded residuated lattice ordered monoids (monoids) are common generalizations of -algebras, i.e., algebras of the propositional basic fuzzy logic, and Heyting algebras, i.e., algebras of the propositional intuitionistic logic. From the point of view of uncertain information, sets of provable formulas in inference systems could be described by fuzzy filters of the corresponding...
Commutative idempotent residuated lattices
We investigate the variety of residuated lattices with a commutative and idempotent monoid reduct.
Completions for partially ordered semigroups.
Complex calculus of variations
In this article, we present a detailed study of the complex calculus of variations introduced in [M. Gondran: Calcul des variations complexe et solutions explicites d’équations d’Hamilton–Jacobi complexes. C.R. Acad. Sci., Paris 2001, t. 332, série I]. This calculus is analogous to the conventional calculus of variations, but is applied here to functions in . It is based on new concepts involving the minimum and convexity of a complex function. Such an approach allows us to propose explicit solutions...
Conditions for strong Morita equivalence of partially ordered semigroups
We investigate when a partially ordered semigroup (with various types of local units) is strongly Morita equivalent to a posemigroup from a given class of partially ordered semigroups. Necessary and sufficient conditions for such equivalence are obtained for a series of well-known classes of posemigroups. A number of sufficient conditions for several classes of naturally ordered posemigroups are also provided.
Congruences on ordered groupoids.
Constructing ordered groupoids
Constructing quantales and their modules from monoidal categories
Continuous extension of order-preserving homogeneous maps
Maps defined on the interior of the standard non-negative cone in which are both homogeneous of degree and order-preserving arise naturally in the study of certain classes of Discrete Event Systems. Such maps are non-expanding in Thompson’s part metric and continuous on the interior of the cone. It follows from more general results presented here that all such maps have a homogeneous order-preserving continuous extension to the whole cone. It follows that the extension must have at least...
Continuous monoids and yields of infinite trees
Decomposition of commutative ordered semigroups into archimedean components.
Demi-groupes 0-simples et complètement 0-simples totalement ordonnés. Application aux demi-groupes de matrices de Rees
Demi-groupes et catégories à involution
Die Verbände mit nichteinfacher Funktionenalgebra.