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Discussiones Mathematicae - General Algebra and Applications
Article . 2022 . Peer-reviewed
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Discussiones Mathematicae - General Algebra and Applications
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Article . 2022
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Disjunctive ideals of Almost Distributive Lattices

Disjunctive ideals of almost distributive lattices
descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2022 English Publisher:University of Zielona Góra, PolandJournal:Discussiones Mathematicae - General Algebra and Applications, volume 42, page 159 (issn: 1509-9415, eissn: 2084-0373, Copyright policy )
Authors: Rafi N.; Srujana M.; Rao T. Srinivasa;

doi: 10.7151/dmgaa.1384

Disjunctive ideals of Almost Distributive Lattices

Abstract

Summary: The concept of disjunctive ideals is introduced in an Almost Distributive Lattice (ADL). It is proved that the set of all disjunctive ideals of an ADL forms a complete lattice. A necessary and sufficient condition is derived for an inverse homomorphic image of a disjunctive ideal of an ADL to be again a disjunctive ideal. Later, the concept of strongly disjunctive ideals is introduced in an ADL and their properties are studied. Some equivalent conditions are established for the set of all strongly disjunctive ideals to convert into a sublattice of the ideal lattice.

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Keywords

Lattice ideals, congruence relations, almost distributive lattice (adl), disjunctive ideal, normal adl, normal ADL, minimal prime ideal, almost distributive lattice (ADL), 06d15, normal prime ideal, QA1-939, Other generalizations of distributive lattices, strongly disjunctive ideal, 06d99, Complete lattices, completions, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
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