Cantor-Bernstein theorem for -algebras
Cardinal properties of lattice ordered groups
Cardinal sums of linearly ordered groups
Cardinality of the system of all sequential convergences on an Abelian lattice ordered group
Categorical structures enriched in a quantaloid: categories, distributors and functors.
Categorical structures enriched in a quantaloid : regular presheaves, regular semicategories
Categorical structures enriched in a quantaloid: tensored and cotensored categories.
Causal structures in linear spaces.
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.
Characterisations of Semi-Prime Archimedean f-algebras.
Characterization of all order relations in direct sums of ordered groups.
Characterization of matrix types of ultramatricial algebras.
Characterizations of balayages.
Characterizing ordered quasi-ideals of ordered -semigroups
Characterizing ordered semigroups by means of intuitionistic fuzzy bi-ideals.
Circular totally semi-ordered groups
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...
Closed and open sets in topologies induced by lattice ordered vector groups
Closed convex -subgroups and radical classes of convergence -groups
In this paper we prove that the system of all closed convex -subgroups of a convergence -group is a Brouwer lattice and that a similar result is valid for radical classes of convergence -groups.