Remarks on powers of lattices
Remarks on products of σ-ideals
Remarks on pseudo MV-algebras
Pseudo MV-algebras (see e.g., [4, 6, 8]) are non-commutative extension of MV-algebras. We show that every pseudo MV-algebra is isomorphic to the algebra of action functions where the binary operation is function composition, zero is x ∧ y and unit is x. Then we define the so-called difference functions in pseudo MV-algebras and show how a pseudo MV-algebra can be reconstructed by them.
Remarks on -independence of Stone algebras
Remarks on quasivarieties of algebras
Remarks on representation of fuzzy quantum posets
Remarks on special ideals in lattices
The author studies some characteristic properties of semiprime ideals. The semiprimeness is also used to characterize distributive and modular lattices. Prime ideals are described as the meet-irreducible semiprime ideals. In relatively complemented lattices they are characterized as the maximal semiprime ideals. -radicals of ideals are introduced and investigated. In particular, the prime radicals are determined by means of -radicals. In addition, a necessary and sufficient condition for the equality...
Remarks on subdirect representations in categories
Remarks on the order for quantum observables
Remarks on the sobriety of Scott topology and weak topology on posets
We give some necessary and sufficient conditions for the Scott topology on a complete lattice to be sober, and a sufficient condition for the weak topology on a poset to be sober. These generalize the corresponding results in [1], [2] and [4].
Remarks on the Stone Spaces of the Integers and the Reals without AC
In ZF, i.e., the Zermelo-Fraenkel set theory minus the Axiom of Choice AC, we investigate the relationship between the Tychonoff product , where 2 is 2 = 0,1 with the discrete topology, and the Stone space S(X) of the Boolean algebra of all subsets of X, where X = ω,ℝ. We also study the possible placement of well-known topological statements which concern the cited spaces in the hierarchy of weak choice principles.
Remarks to a modification of Ramsey-type theorems
Remarque sur les treillis complets pseudo complémentes
Remarques sur la théorie des multitreillis VI (Contribution à la théorie des structures algébriques ordonnées)
Remarques sur les propriétés métriques des ensembles ordonnés
Representable dually residuated lattice-ordered monoids
Dually residuated lattice-ordered monoids (DRl-monoids) generalize lattice-ordered groups and include also some algebras related to fuzzy logic (e.g. GMV-algebras and pseudo BL-algebras). In the paper, we give some necessary and sufficient conditions for a DRl-monoid to be representable (i.e. a subdirect product of totally ordered DRl-monoids) and we prove that the class of representable DRl-monoids is a variety.
Representable posets and their order components
Representation and duality for Hilbert algebras
In this paper we introduce a special kind of ordered topological spaces, called Hilbert spaces. We prove that the category of Hilbert algebras with semi-homomorphisms is dually equivalent to the category of Hilbert spaces with certain relations. We restrict this result to give a duality for the category of Hilbert algebras with homomorphisms. We apply these results to prove that the lattice of the deductive systems of a Hilbert algebra and the lattice of open subsets of its dual Hilbert space, are...
Representation and duality of multiplication operators on archimedean Riesz spaces
Représentation de quasi-ordres et de relations probabilistes transitives sous forme standard et méthodes d'approximation