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A characterization of 1-, 2-, 3-, 4-homomorphisms of ordered sets

Radomír Halaš, Daniel Hort (2003)

Czechoslovak Mathematical Journal

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

Ivan Chajda (2009)

Mathematica Bohemica

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.

Francesc Esteva (1977)

Stochastica

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 finite Stone pseudocomplemented ordered sets

Radomír Halaš (1996)

Mathematica Bohemica

A distributive pseudocomplemented set S [2] is called Stone if for all a S the condition L U ( a * , a * * ) = S holds. It is shown that in a finite case S is Stone iff the join of all distinct minimal prime ideals of S is equal to S .

A characterization of uninorms on bounded lattices via closure and interior operators

Gül Deniz Çayli (2023)

Kybernetika

Uninorms on bounded lattices have been recently a remarkable field of inquiry. In the present study, we introduce two novel construction approaches for uninorms on bounded lattices with a neutral element, where some necessary and sufficient conditions are required. These constructions exploit a t-norm and a closure operator, or a t-conorm and an interior operator on a bounded lattice. Some illustrative examples are also included to help comprehend the newly added classes of uninorms.

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