The theory of commuting subalgebras of complete Heyting algebras
type: Item
instance of: scholarly article
title: The theory of commuting subalgebras of complete Heyting algebras
zbMATH Open document ID: 0922.06013
author: Jeffrey Thomas Crants
author: Catherine Yan
published in: Advances in Mathematics
publication date: 1999-05-18T00:00:00Z
review text: The authors give a detailed analysis of the lattice of commuting subalgebras of a Heyting algebra and develop a proof theory for these lattices. The main result is a completeness theorem for inequalities and, more generally, Horn sentences valid in all the lattices.
Mathematics Subject Classification ID: 06D20
Mathematics Subject Classification ID: 06E99
Mathematics Subject Classification ID: 08A30
zbMATH DE Number: 1236403
zbMATH Keywords: Heyting algebra
zbMATH Keywords: Boolean algebra
zbMATH Keywords: commuting subalgebras
zbMATH Keywords: deduction rule
zbMATH Keywords: Horn sentence
reviewed by: Leo Esakia
MaRDI profile type: Publication
full work available at URL: aima.1998.1758
OpenAlex ID: W2015585734
cites work: Q5331549
cites work: Selected papers on algebra and topology. Ed. by Gian-Carlo Rota and Joseph S. Oliveira
cites work: Q3956998
cites work: Q4896505
cites work: Q4165427
cites work: Proof theory for linear lattices
cites work: Q5721231
cites work: Q3965241
cites work: On the representation of lattices
cites work: Representation of Modular Lattices and Of Relation Algebras
cites work: Theory of equivalence relations
cites work: The Lattice of Subalgebras of a Boolean Algebra
cites work: Q5585437
cites work: Commuting quasi-order relations
cites work: Distributive laws for commuting equivalence relations
DOI: 10.1006/AIMA.1998.1758
Recommended article: Subalgebras of Heyting and De Morgan Heyting algebras
Recommended article: Maximal subalgebras of Heyting algebras
Recommended article: The subalgebra lattice of a Heyting algebra
Recommended article: ON CERTAIN COMMUTATIVE SUBALGEBRAS OF A UNIVERSAL ENVELOPING ALGEBRA
Recommended article: Q3357723
Recommended article: Relative Commutants of Hecke Algebra Subfactors
Recommended article: On some compatible operations on Heyting algebras
Recommended article: Q4869432
Recommended article: Q5844486
description: scientific article; zbMATH DE number 1236403