Results 41 to 50 of about 95 (81)
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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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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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On the lattice of quasivarieties of Sugihara algebras
Studia Logica, 1986A Sugihara algebra is any algebra belonging to the variety \({\mathcal S}\) generated by the following algebra: \({\mathfrak S}=(Z,\wedge,\vee,\to,^-)\), where Z is the set of integers with the usual ordering, \(\bar x=-x\) and \(x\to y=\bar x\vee y\) if \(x\leq y\), \(x\to y=\bar x\wedge y\) otherwise.
Willem J. Blok, Wieslaw Dziobiak
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Quasivarieties of Graphs and Independent Axiomatizability
Siberian Advances in Mathematics, 2018Summary: In the present article, we continue to study the complexity of the lattice of quasivarieties of graphs. For every quasivariety \(K\) of graphs that contains a non-bipartite graph, we find a subquasivariety \(K'\subset K\) such that there exist \(2^{\omega}\) subquasivarieties \(K'' \in L_q(K')\) without covers (hence, without independent bases
Kravchenko, A. V., Yakovlev, A. V.
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Siberian Mathematical Journal, 1994
By a graph we mean a model of a binary predicate \(\rho(x,y)\). Many well-known properties of binary relations, such as reflexivity, symmetry, antisymmetry, transitivity, etc., are written down by means of quasiidentities. Such important classes of graphs as the class of all partial orders, the class of models of an equivalence relation, the class of ...
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By a graph we mean a model of a binary predicate \(\rho(x,y)\). Many well-known properties of binary relations, such as reflexivity, symmetry, antisymmetry, transitivity, etc., are written down by means of quasiidentities. Such important classes of graphs as the class of all partial orders, the class of models of an equivalence relation, the class of ...
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Quasivariety of special jordan algebras
Algebra and Logic, 1983It is well known that the class of all special Jordan algebras does not form a variety of algebras, but it is not difficult to see that this class forms a quasivariety of algebras. The natural question then arises whether this quasivariety can be defined by a finite number of quasi- identities.
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Model companions of the quasivarieties of polygons
Siberian Mathematical Journal, 1998The author studies the existence problem for model companions of quasivarieties of polygons. Let \(\mathcal H\) be the class of polygons which possesses the amalgamation property and the congruence extension property. In the article under review, the existence of a model companion for \(\mathcal H\) is proven to be equivalent to each of the following ...
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