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Characterization of posets of intervals

Judita Lihová (2000)

Archivum Mathematicum

If A is a class of partially ordered sets, let P ( A ) denote the system of all posets which are isomorphic to the system of all intervals of A for some A ∈ A . We give an algebraic characterization of elements of P ( A ) for A being the class of all bounded posets and the class of all posets A satisfying the condition that for each a ∈ A there exist a minimal element u and a maximal element v with u ≤ a ≤ v , respectively.

Characterization of the order induced by uninorm with the underlying drastic product or drastic sum

Zhi-qiang Liu (2024)

Kybernetika

In this article, we investigate the algebraic structures of the partial orders induced by uninorms on a bounded lattice. For a class of uninorms with the underlying drastic product or drastic sum, we first present some conditions making a bounded lattice also a lattice with respect to the order induced by such uninorms. And then we completely characterize the distributivity of the lattices obtained.

Characterizations of 0-distributive posets

Vinayak V. Joshi, B. N. Waphare (2005)

Mathematica Bohemica

The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.

Characterizations of the 0 -distributive semilattice

P. Balasubramani (2003)

Mathematica Bohemica

The 0 -distributive semilattice is characterized in terms of semiideals, ideals and filters. Some sufficient conditions and some necessary conditions for 0 -distributivity are obtained. Counterexamples are given to prove that certain conditions are not necessary and certain conditions are not sufficient.

Characterizations of totally ordered sets by their various endomorphisms

Daniel Hort, Jan Chvalina, Jiří Moučka (2002)

Czechoslovak Mathematical Journal

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.

Choice principles in Węglorz’ models

N. Brunner, Paul Howard, Jean Rubin (1997)

Fundamenta Mathematicae

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

Ivan Chajda, Miroslav Kolařík, Helmut Länger (2024)

Mathematica Bohemica

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....

Currently displaying 61 – 80 of 319