Priestley-style duality for DN-algebras

The aim of this article is to develop a Priestley-style duality for the variety of DN-algebras. In order to achieve this, we use the concept of free distributive lattice extension of a DN-algebra. We establish a connection with the Priestley duality for distributive lattices. Finally, we present top...

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Bibliographic Details
Published inAlgebra universalis Vol. 85; no. 1
Main Author González, Luciano J.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.02.2024
Springer Nature B.V
Subjects
Algebra
Congruences
Lattices (mathematics)
Mathematics
Mathematics and Statistics
06A12
06D75
Distributive lattice
06D99
DN-algebra
06F99
Distributive nearlattice
Priestley space
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Summary:The aim of this article is to develop a Priestley-style duality for the variety of DN-algebras. In order to achieve this, we use the concept of free distributive lattice extension of a DN-algebra. We establish a connection with the Priestley duality for distributive lattices. Finally, we present topological descriptions for the lattice of filters, for the lattice of congruences, and for certain kinds of subalgebras of a DN-algebra.
ISSN:0002-5240
1420-8911
DOI:10.1007/s00012-023-00838-0