The space of minimal prime D−filters of Almost Distributive Lattices

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2024 English Publisher:University of Zielona Góra, PolandJournal:Discussiones Mathematicae - General Algebra and Applications, volume 44, page 343 (issn: 1509-9415, eissn: 2084-0373,

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Authors: Noorbhasha Rafi; Pavuluri Vijaya Saradhi; Mothukuri Balaiah;

doi: 10.7151/dmgaa.1467

The space of minimal prime D−filters of Almost Distributive Lattices

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Abstract

Summary: The concept of \(D\)-filters is introduced in an Almost Distributive Lattice (ADL) and studied their properties. An equivalency is established between the minimal prime \(D\)-filters of an ADL and its quotient ADL with respect to a congruence. Finally, some properties of prime \(D\)-filters and minimal prime \(D\)-filters of an ADL are studied topologically.

Keywords

Hausdorff space, \(D\)-normal ADL, compact, almost distributive lattice, congruence, QA1-939, Other generalizations of distributive lattices, \(D\)-filter, closure, Mathematics, prime filter

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