-completeness and fixpoint properties
-ideals in -distributive posets
The concept of a -ideal in -distributive posets is introduced. Several properties of -ideals in -distributive posets are established. Further, the interrelationships between -ideals and -ideals in -distributive posets are investigated. Moreover, a characterization of prime ideals to be -ideals in -distributive posets is obtained in terms of non-dense ideals. It is shown that every -ideal of a -distributive meet semilattice is semiprime. Several counterexamples are discussed.
0-distributive posets
Several characterizations of 0-distributive posets are obtained by using the prime ideals as well as the semiprime ideals. It is also proved that if every proper -filter of a poset is contained in a proper semiprime filter, then it is -distributive. Further, the concept of a semiatom in 0-distributive posets is introduced and characterized in terms of dual atoms and also in terms of maximal annihilator. Moreover, semiatomic 0-distributive posets are defined and characterized. It is shown that...
A Bruhat order for the class of -matrices with row sum vector and column sum vector .
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 congruence kernels in pseudocomplemented semilattices
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 polarities whose polar lattice is orthomodular
A characterization of semilattices
A characterization of tolerance-distributive tree semilattices
A characterization of well-orders
A class of -preduals which are isomorphic to quotients of
For every countable ordinal α, we construct an -predual which is isometric to a subspace of and isomorphic to a quotient of . However, is not isomorphic to a subspace of .
A common approach to directoids with an antitone involution and D-quasirings
We introduce the so-called DN-algebra whose axiomatic system is a common axiomatization of directoids with an antitone involution and the so-called D-quasiring. It generalizes the concept of Newman algebras (introduced by H. Dobbertin) for a common axiomatization of Boolean algebras and Boolean rings.
A completion for partially ordered abelian groups.
A computation of positive one-peak posets that are Tits-sincere
A complete list of positive Tits-sincere one-peak posets is provided by applying combinatorial algorithms and computer calculations using Maple and Python. The problem whether any square integer matrix is ℤ-congruent to its transpose is also discussed. An affirmative answer is given for the incidence matrices and the Tits matrices of positive one-peak posets I.
A constructive characterization of the lattices of all retractions, preclosure, quasi-closure and closure operators on a complete lattice
A continuous lattice L with DID(L) incomplete.