Sheaves on a quantale
Simple and subdirectly irreducibles bounded distributive lattices with unary operators.
Simple games in Łukasiewicz calculus and their cores
We propose a generalization of simple coalition games in the context of games with fuzzy coalitions. Mimicking the correspondence of simple games with non-constant monotone formulas of classical logic, we introduce simple Łukasiewicz games using monotone formulas of Łukasiewicz logic, one of the most prominent fuzzy logics. We study the core solution on the class of simple Łukasiewicz games and show that cores of such games are determined by finitely-many linear constraints only. The non-emptiness...
Singular operations on algebras (generalized contractions)
Sober spaces and continuations.
Some properties of strongly normal lattices
Some remarks on certain classes of semilattices.
Some remarks on distributive semilattices
In this paper we shall give a survey of the most important characterizations of the notion of distributivity in semilattices with greatest element and we will present some new ones through annihilators and relative maximal filters. We shall also simplify the topological representation for distributive semilattices given in Celani S.A., Topological representation of distributive semilattices, Sci. Math. Japonicae online 8 (2003), 41–51, and show that the meet-relations are closed under composition....
Some remarks on Post algebras
Some results on dimension theory: Universal spaces
Spaces with Boolean assemblies
Spectra of autometrized lattice algebras
Autometrized algebras are a common generalization e.g. of commutative lattice ordered groups and Brouwerian algebras. In the paper, spectra of normal autometrized lattice ordered algebras (i.e. topologies of sets (and subsets) of their proper prime ideals) are studied. Especially, the representable dually residuated lattice ordered semigroups are examined.
Spectra of rings and lattices.
Spectral topologies of dually residuated lattice-ordered monoids
Dually residuated lattice-ordered monoids (-monoids for short) generalize lattice-ordered groups and include for instance also -algebras (pseudo -algebras), a non-commutative extension of -algebras. In the present paper, the spectral topology of proper prime ideals is introduced and studied.
Split structures.
Stable closed frame homomorphisms
Standard completions for quasiordered sets.
State-homomorphisms on -algebras
Riečan [12] and Chovanec [1] investigated states in -algebras. Earlier, Riečan [11] had dealt with analogous ideas in -posets. In the monograph of Riečan and Neubrunn [13] (Chapter 9) the notion of state is applied in the theory of probability on -algebras. We remark that a different definition of a state in an -algebra has been applied by Mundici [9], [10] (namely, the condition (iii) from Definition 1.1 above was not included in his definition of a state; in other words, only finite additivity...
States on basic algebras
States on commutative basic algebras were considered in the literature as generalizations of states on MV-algebras. It was a natural question if states exist also on basic algebras which are not commutative. We answer this question in the positive and give several examples of such basic algebras and their states. We prove elementary properties of states on basic algebras. Moreover, we introduce the concept of a state-morphism and characterize it among states. For basic algebras which are the certain...
States on pseudo-effect algebras with general comparability