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A choice-free proof of Mal’cev’s theorem on quasivarieties
Algebra UniversalisIn 1966, Mal’cev proved that a class K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt ...
Guozhen Shen
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UNREASONABLE LATTICES OF QUASIVARIETIES
International Journal of Algebra and Computation, 2012A quasivariety is a universal Horn class of algebraic structures containing the trivial structure. The set [Formula: see text] of all subquasivarieties of a quasivariety [Formula: see text] forms a complete lattice under inclusion. A lattice isomorphic to [Formula: see text] for some quasivariety [Formula: see text] is called a lattice of ...
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Complexity of Quasivariety Lattices
Algebra and Logic, 2015A quasivariety \(\mathbf K\) is a class of algebraic systems closed under isomorphisms, subsystems, direct products, and ultraproducts. The quasivarieties contained in a quasivariety \(\mathbf K\) form a complete lattice \(\mathbf{Lq(K)}\) under inclusion. Quasivariety lattices might be highly complex. A measure of complexity is given by the notion of \
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Relationships among quasivarieties induced by the min networks on inverse semigroups
Semigroup Forum, 2020A congruence on an inverse semigroup S is determined uniquely by its kernel and trace. Denoting by ρk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage ...
Ying-Ying Feng +2 more
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On quasivarieties and varieties as categories
Studia Logica, 2004The paper deals with a classical topic of category theory because the first characterizations of varieties and quasivarieties of universal algebras were found by F. W. Lawvere and J. R. Isbell in the early 1960s. The author weakens their assumptions with the aim to get ``optimum'' characterizations. The motivating idea is to combine cocompleteness with
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SUBFUNCTORS ASSOCIATED WITH QUASIVARIETIES
1984Quasivarieties of algebras are characterized as SP-classes closed under a certain construction of directed unions of congruences.
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Quasivarieties of Metric Algebras
Algebra and Logic, 2003The author introduces the concepts of a continuous family of quasi-identities and of a continuous quasivariety. For continuous quasivarieties, a characterization theorem and an analog of the Birkhoff theorem on subdirect decomposition are proven.
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Quasivarieties of Cantor algebras
Algebra Universalis, 2001A variety \(\mathcal V\) is minimal if it is equationally complete. A quasivariety is called \(Q\)-universal if for every quasivariety \(K\) of a finite type the lattice \(L_Q (K)\) of all subquasivarieties is a homomorphic image of \(L_Q (Q)\). The author studies varieties \(C_{mn}\) of the so-called Cantor algebras (firstly treated in the early 60s ...
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Equivalents for a Quasivariety to be Generated by a Single Structure
Studia Logica, 2009In \textit{A. I. Mal'tsev}'s article [Algebra Logika 5, No. 3, 3--9 (1966; Zbl 0248.08006)], there can be found a condition for a quasivariety to be generated by a single structure, namely, the embedding property for nontrivial structures, which states that if \(A,B\in \mathcal{K}\) are nontrivial, then there exists \(C\in \mathcal{K}\) such that \(A,B\
Wieslaw Dziobiak +2 more
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Siberian Mathematical Journal, 1999
Let \(\mathcal E\) be a given group-theoretical property and \(G\) be some group. We say that the group \(G\) has the property \(L({\mathcal E})\) generated by the property \(\mathcal E\) if, for every element \(x\in G\), the normal closure \((x)^G\) has the property \(\mathcal E\). The property \(L({\mathcal E})\) is called the Levy property.
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Let \(\mathcal E\) be a given group-theoretical property and \(G\) be some group. We say that the group \(G\) has the property \(L({\mathcal E})\) generated by the property \(\mathcal E\) if, for every element \(x\in G\), the normal closure \((x)^G\) has the property \(\mathcal E\). The property \(L({\mathcal E})\) is called the Levy property.
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