The varieties defined by \(P\)-compatible identities of modular ortholattices
type: Item
instance of: scholarly article
title: The varieties defined by \(P\)-compatible identities of modular ortholattices
zbMATH Open document ID: 1210.06006
author: Krystyna Mruczek-Nasieniewska
published in: Studia Logica
publication date: 2010-12-01T00:00:00Z
review text: Consider the variety MOL of modular ortholattices with the set \(F:=\{\vee,\wedge,'\}\) of operation symbols and let \(P\) be a partition of \(F\) and \(p=q\) an identity in MOL. The identity \(p=q\) is called \(P\)-compatible if either \(p\) and \(q\) are the same variable or \(p\) and \(q\) are not variables and the outermost operation symbol of \(p\) and that of \(q\) belong to the same block of \(P\). ``Externally compatible'' means \(P\)-compatible where \(P\) consists of singletons only. Let MOL\(_P\) (MOL\(_{Ex}\)) denote the variety defined by the set of all \(P\)-compatible (externally compatible) identities satisfied in MOL. Equational bases of MOL\(_{Ex}\) are explicitly stated, MOL\(_P\) is semantically characterized, and the lattice of some subvarieties of MOL\(_{Ex}\) is described.
reviewed by: Helmut Länger
Mathematics Subject Classification ID: 06C15
Mathematics Subject Classification ID: 08B15
zbMATH DE Number: 5822063
zbMATH Keywords: variety
zbMATH Keywords: modular ortholattice
zbMATH Keywords: \(P\)-compatible identity
zbMATH Keywords: externally compatible identity
zbMATH Keywords: equational base
zbMATH Keywords: semantics
zbMATH Keywords: lattice of subvarieties
MaRDI profile type: Publication
full work available at URL: s11225-010-9255-5
OpenAlex ID: W1975208105
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DOI: 10.1007/S11225-010-9255-5
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description: scientific article; zbMATH DE number 5822063