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0 -ideals in 0 -distributive posets

Khalid A. Mokbel (2016)

Mathematica Bohemica

The concept of a 0 -ideal in 0 -distributive posets is introduced. Several properties of 0 -ideals in 0 -distributive posets are established. Further, the interrelationships between 0 -ideals and α -ideals in 0 -distributive posets are investigated. Moreover, a characterization of prime ideals to be 0 -ideals in 0 -distributive posets is obtained in terms of non-dense ideals. It is shown that every 0 -ideal of a 0 -distributive meet semilattice is semiprime. Several counterexamples are discussed.

0-distributive posets

Khalid A. Mokbel, Vilas S. Kharat (2013)

Mathematica Bohemica

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 l -filter of a poset is contained in a proper semiprime filter, then it is 0 -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 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 common approach to directoids with an antitone involution and D-quasirings

Ivan Chajda, Miroslav Kolařík (2008)

Discussiones Mathematicae - General Algebra and Applications

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.

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