Characterizations of certain classes of posets having Gs-lattices of a relatively small size
Characterizations of certain general and reproductive solutions of arbitrary equations
Characterizations of effective sets and nonexpansive multipliers in conditionally complete and infinitely distributive partially ordered sets.
Characterizations of nonexpansive multipliers on partially ordered sets
Characterizations of the -distributive semilattice
The -distributive semilattice is characterized in terms of semiideals, ideals and filters. Some sufficient conditions and some necessary conditions for -distributivity are obtained. Counterexamples are given to prove that certain conditions are not necessary and certain conditions are not sufficient.
Characterizations of the anti-exchange closure
Characterizations of totally ordered sets by their various endomorphisms
We characterize totally ordered sets within the class of all ordered sets containing at least three-element chains using a simple relationship between their isotone transformations and the so called 2-, 3-, 4-endomorphisms which are introduced in the paper. Another characterization of totally ordered sets within the class of ordered sets of a locally finite height with at least four-element chains in terms of the regular semigroup theory is also given.
Characterizing ordered quasi-ideals of ordered -semigroups
Characterizing ordered semigroups by means of intuitionistic fuzzy bi-ideals.
Characterizing triplets for modular pseudocomplemented ordered sets
Choice principles in Węglorz’ models
Węglorz' models are models for set theory without the axiom of choice. Each one is determined by an atomic Boolean algebra. Here the algebraic properties of the Boolean algebra are compared to the set theoretic properties of the model.
c-ideals in complemented posets
In their recent paper on posets with a pseudocomplementation denoted by the first and the third author introduced the concept of a -ideal. This concept is in fact an extension of a similar concept introduced in distributive pseudocomplemented lattices and semilattices by several authors, see References. Now we apply this concept of a c-ideal (dually, c-filter) to complemented posets where the complementation need neither be antitone nor an involution, but still satisfies some weak conditions....
Circular totally semi-ordered groups
Classes équationnelles de treillis orthomodulaires liées aux états
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...
Classification of the regular De Morgan algebras of fuzzy sets.
A characterization of regular lattices of fuzzy sets and their isomorphisms is given in Part I. A characterization of involutions on regular lattices of fuzzy sets and the isomorphisms of De Morgan algebras of fuzzy sets is given in Part II. Finally all classes of De Morgan algebras of fuzzy sets with respect to isomorphisms are completely described.
Classification systems and their lattice
We define and study classification systems in an arbitrary CJ-generated complete lattice L. Introducing a partial order among the classification systems of L, we obtain a complete lattice denoted by Cls(L). By using the elements of the classification systems, another lattice is also constructed: the box lattice B(L) of L. We show that B(L) is an atomistic complete lattice, moreover Cls(L)=Cls(B(L)). If B(L) is a pseudocomplemented lattice, then every classification system of L is independent and...
Clones closed with respect to permutation groups or transformation semigroups.
Closed and open sets in topologies induced by lattice ordered vector groups