Residuated structures and orthomodular lattices
type: Item
instance of: scholarly article
title: Residuated structures and orthomodular lattices
zbMATH Open document ID: 1487.03074
author: Davide Fazio
author: Antonio Ledda
author: Francesco Paoli
published in: Studia Logica
publication date: 2021-12-27T00:00:00Z
review text: The authors introduce the variety of pointed left-residuated \(\ell\)-groupoids as a common generalization of various classes of residuated structures (e.g., \(\ell\)-groups, Heyting algebras, MV-algebras, De Morgan monoids) and quantum structures (e.g., orthomodular lattices, lattice effect algebras, basic algebras). They study this variety and the lattice of its subvarieties, develop the theory of left nuclei for these structures and extend the theory of join-completions of residuated \(\ell\)-groupoids to the left-residuated case. The latter gives a new proof of MacLaren's theorem for orthomodular lattices.
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 03D25
Mathematics Subject Classification ID: 06C15
Mathematics Subject Classification ID: 03G27
Mathematics Subject Classification ID: 06B23
zbMATH DE Number: 7450670
zbMATH Keywords: residuated groupoid
zbMATH Keywords: left-residuated groupoid
zbMATH Keywords: residuated lattice
zbMATH Keywords: orthomodular lattice
zbMATH Keywords: quantum structure
zbMATH Keywords: completion
zbMATH Keywords: Dedekind-MacNeille completion
reviewed by: Josef Tkadlec
MaRDI profile type: Publication
full work available at URL: s11225-021-09946-1
OpenAlex ID: W3153150069
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DOI: 10.1007/S11225-021-09946-1
description: scientific article; zbMATH DE number 7450670