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
A characterization of ordered groups by means of segments
A characterization of polarities whose lattice of polars is Boolean
A characterization of polarities whose polar lattice is orthomodular
A characterization of quantic quantifiers in orthomodular lattices.
A characterization of regular le-semigroups.
A characterization of semilattices
A characterization of subgroup lattices of finite abelian groups.
A characterization of tolerance-distributive tree semilattices
A characterization of uninorms on bounded lattices via closure and interior operators
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.