Structure of quasivariety lattices. I: Independent axiomatizability
type: Item
instance of: scholarly article
title: Structure of quasivariety lattices. I: Independent axiomatizability
zbMATH Open document ID: 1439.08008
published in: Algebra and Logic
publication date: 2019-12-06T00:00:00Z
review text: A quasivariety \(K\) has an \(\omega \)-independent quasi-equational basis in a quasivariety \(M\) if there are a basis \(\Phi \) of \(K\) in \(M\) and a partition \(\Phi =\cup_ {n<\omega} \Phi_n\) such that for every \(i\) \(\Phi\setminus\Phi_i\) is not a basis of \(K\) in \(M\). A quasivariety \(K\) is a \(Q\)-universal if its lattice of subquasivarieties has, as a homomorphic image of a sublattice, the lattice of subquasivarieties of any quasivariety of algebras of finite type. The authors find a sufficient condition for a quasivariety \(K\) to have continuum many subquasivarieties that have no independent quasi-equational bases in \(K\) but have \(\omega\)-independent quasi-equational bases in \(K\). This condition also implies that \(K\) is \(Q\)-universal.
Mathematics Subject Classification ID: 08C15
Mathematics Subject Classification ID: 08B15
zbMATH DE Number: 7140958
zbMATH Keywords: independent basis
zbMATH Keywords: quasi-identity
zbMATH Keywords: quasivariety
zbMATH Keywords: quasivariety lattice
zbMATH Keywords: \(Q\)-universality
author: Aleksandr Vladimirovich Kravchenko
author: A. M. Nurakunov
author: M. V. Schwidefsky
reviewed by: Alexander Ivanovich Budkin
MaRDI profile type: Publication
full work available at URL: s10469-019-09516-4
OpenAlex ID: W2924675113
cites work: Q5834648
cites work: Filters in lattices of quasivarieties of algebraic systems
cites work: ON FILTERS IN THE LATTICE OF QUASIVARIETIES OF GROUPS
cites work: Covers in lattices of quasivarieties and independent axiomatizability
cites work: Quasivarieties of groups having no coverings
cites work: Lattices of quasivarieties of unars
cites work: Quasivarieties of graphs
cites work: The lattice of quasivarieties of semigroups
cites work: Q-Universal Quasivarieties of Algebras
cites work: On lattice identities satisfied in subquasivariety lattices of varieties of modular lattices
cites work: Structure of lattices of varieties and lattices of quasivarieties: Similarity and difference. II
cites work: Q4935937
cites work: Finite-to-finite universal quasivarieties are \(Q\)-universal.
cites work: Unreasonable lattices of quasivarieties
cites work: Quasivariety lattices of pointed abelian groups.
cites work: Complexity of quasivariety lattices.
cites work: On the complexity of quasivariety lattices
cites work: Universally axiomatizable subclasses of locally finite classes of models
cites work: Q5609363
cites work: On representation of finite lattices
cites work: Q5628181
cites work: Congruence Relations in Direct Products
cites work: Q4517140
Wikidata QID: Q128206963
DOI: 10.1007/S10469-019-09516-4
description: scientific article; zbMATH DE number 7140958