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.
A characterization for all interval doubling schemes of the lattice of permutations.
A characterization of 1-, 2-, 3-, 4-homomorphisms of ordered sets
We characterize totally ordered sets within the class of all ordered sets containing at least four-element chains. We use a simple relationship between their isotone transformations and the so called 1-endomorphism which is introduced in the paper. Later we describe 1-, 2-, 3-, 4-homomorphisms of ordered sets in the language of super strong mappings.
A characterization of commutative basic algebras
A basic algebra is an algebra of the same type as an MV-algebra and it is in a one-to-one correspondence to a bounded lattice having antitone involutions on its principal filters. We present a simple criterion for checking whether a basic algebra is commutative or even an MV-algebra.
A characterization of complete atomic Boolean algebra.
In this note we give a characterization of complete atomic Boolean algebras by means of complete atomic lattices. We find that unicity of the representation of the maximum as union of atoms and Lambda-infinite distributivity law are necessary and sufficient conditions for the lattice to be a complete atomic Boolean algebra.
A characterization of complete bi-Brouwerian lattices
A characterization of congruence kernels in pseudocomplemented semilattices
A characterization of distributive lattices by tolerance lattices
A characterization of finite posets of the width at most three with the fixed point property
A characterization of finite Stone pseudocomplemented ordered sets
A distributive pseudocomplemented set [2] is called Stone if for all the condition holds. It is shown that in a finite case is Stone iff the join of all distinct minimal prime ideals of is equal to .
A characterization of inductive posets
A characterization of modular lattices