-completeness and fixpoint properties
-distributive function lattices
It is known that for a nonempty topological space and a nonsingleton complete lattice endowed with the Scott topology, the partially ordered set of all continuous functions from into is a continuous lattice if and only if both and the open set lattice are continuous lattices. This result extends to certain classes of -distributive lattices, where is a subset system replacing the system of all directed subsets (for which the -distributive complete lattices are just the continuous...
-fuzzy ideals in ordered semigroups.
-median
-multipliers and the localization of MV-algebras.
-theories of Boolean algebras
-structures applied to closed ideals in BCH-algebras.
-subalgebras in BCK/BCI-algebras based on point -structures.
-ideals in -distributive posets
The concept of a -ideal in -distributive posets is introduced. Several properties of -ideals in -distributive posets are established. Further, the interrelationships between -ideals and -ideals in -distributive posets are investigated. Moreover, a characterization of prime ideals to be -ideals in -distributive posets is obtained in terms of non-dense ideals. It is shown that every -ideal of a -distributive meet semilattice is semiprime. Several counterexamples are discussed.
0-distributive posets
Several characterizations of 0-distributive posets are obtained by using the prime ideals as well as the semiprime ideals. It is also proved that if every proper -filter of a poset is contained in a proper semiprime filter, then it is -distributive. Further, the concept of a semiatom in 0-distributive posets is introduced and characterized in terms of dual atoms and also in terms of maximal annihilator. Moreover, semiatomic 0-distributive posets are defined and characterized. It is shown that...
2-normalization of lattices
Let be a type of algebras. A valuation of terms of type is a function assigning to each term of type a value . For , an identity of type is said to be -normal (with respect to valuation ) if either or both and have value . Taking with respect to the usual depth valuation of terms gives the well-known property of normality of identities. A variety is called -normal (with respect to the valuation ) if all its identities are -normal. For any variety , there is a least...
A basis of the conjunctively polynomial-like Boolean functions.
A binary operation-based representation of a lattice
In this paper, we study and characterize some properties of a given binary operation on a lattice. More specifically, we show necessary and sufficient conditions under which a binary operation on a lattice coincides with its meet (resp. its join) operation. Importantly, we construct two new posets based on a given binary operation on a lattice and investigate some cases that these two posets have a lattice structure. Moreover, we provide some representations of a given lattice based on these new...
A Bruhat order for the class of -matrices with row sum vector and column sum vector .
A Cantor-Bernstein theorem for -complete MV-algebras
The Cantor-Bernstein theorem was extended to -complete boolean algebras by Sikorski and Tarski. Chang’s MV-algebras are a nontrivial generalization of boolean algebras: they stand to the infinite-valued calculus of Łukasiewicz as boolean algebras stand to the classical two-valued calculus. In this paper we further generalize the Cantor-Bernstein theorem to -complete MV-algebras, and compare it to a related result proved by Jakubík for certain complete MV-algebras.
A categorical account of the localic closed subgroup theorem
Given an axiomatic account of the category of locales the closed subgroup theorem is proved. The theorem is seen as a consequence of a categorical account of the Hofmann-Mislove theorem. The categorical account has an order dual providing a new result for locale theory: every compact subgroup is necessarily fitted.
A categorical proof of the equivalence of local compactness and exponentiability in locale theory
A categorical view at generalized concept lattices
We continue in the direction of the ideas from the Zhang’s paper [Z] about a relationship between Chu spaces and Formal Concept Analysis. We modify this categorical point of view at a classical concept lattice to a generalized concept lattice (in the sense of Krajči [K1]): We define generalized Chu spaces and show that they together with (a special type of) their morphisms form a category. Moreover we define corresponding modifications of the image / inverse image operator and show their commutativity...
A certain Galois connection and weak automorphisms
A characterisation of lattice-ordered abelian groups.