Priestley duality for some subalgebra lattices
type: Item
instance of: scholarly article
title: Priestley duality for some subalgebra lattices
zbMATH Open document ID: 0860.06014
DOI: 10.1007/BF00370144
author: Georges Hansoul
published in: Studia Logica
publication date: 1996-06-02T00:00:00Z
review text: The author characterizes Heyting algebras with a modular congruence lattice. His investigations are carried out within the Priestley space \(X\) of such algebras. The author also looks at Heyting algebras with complemented congruence or subalgebra lattices. For example, for finite Heyting spaces \(X\), \(\text{Con} (X)\) is complemented if and only if \(X\) is a tree and for a Heyting algebra \(H\), \(\text{Sub} (H)\) is complemented in case that \(H\) is retractive, i.e., for each epimorphism \(H\to H'\), there is an embedding \(H'\to H\) such that \(H'\to H\to H'\) is the identity map.
Mathematics Subject Classification ID: 06D20
Mathematics Subject Classification ID: 06C05
Mathematics Subject Classification ID: 06C15
Mathematics Subject Classification ID: 06E15
zbMATH DE Number: 883887
zbMATH Keywords: Heyting algebras
zbMATH Keywords: congruence lattice
zbMATH Keywords: Priestley space
zbMATH Keywords: subalgebra lattices
zbMATH Keywords: Heyting spaces
reviewed by: Klaus Kaiser
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 883887