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On atoms in the lattice of quasivarieties
Algebra Universalis, 1987A Q-lattice is a lattice isomorphic to the subquasivariety lattice of a quasivariety of algebraic systems. Every Q-lattice is join semi- distributive. The converse statement is false since every Q-lattice is atomic and its dual is algebraic. The aim of the present paper is to prove the following theorem: ``The join of a finite set X of atoms in any Q ...
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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.
Blok, W. J., Dziobiak, W.
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Complexity of quasivariety lattices for varieties of differential groupoids. II
Siberian Advances in Mathematics, 2009Summary: We continue the study of the lattice of quasivarieties of differential groupoids [for part I see Mat. Tr. 12, No. 1, 26-39 (2009); translation in Sib. Adv. Math. 19, No. 3, 162-171 (2009; Zbl 1249.08012)]. We suggest a method for constructing differential groupoids from graphs.
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ON FILTERS IN THE LATTICE OF QUASIVARIETIES OF GROUPS
Mathematics of the USSR-Izvestiya, 1989See the review in Zbl 0656.20032.
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A Lattice of Quasivarieties of Normal Cryptogroups
Semigroup Forum, 2007A normal cryptogroup S is a completely regular semigroup in which ${\cal H}$ is a congruence and $S/{{\cal H}}$ is a normal band.
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On coatoms in lattices of quasivarieties of algebraic systems
algebra universalis, 2001Let \(qK\) stand for the quasivariety of algebraic systems generated by a class \(K\), let \(L_q(M)\) be the lattice of subquasivarieties contained in a quasivariety \(M\). Coatoms in the lattice \(L_q(M)\) for a finite set \(K\) of finite algebraic systems were studied by \textit{A.\ I.\ Budkin} and \textit{V.\ A.\ Gorbunov} [Algebra Logika 14, 123 ...
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The lattice of quasivarieties of metabelian groups
Algebra and Logic, 1996The author proves that the lattice of quasivarieties contained in the quasivariety of torsion-free groups satisfying the identity \(\forall x\forall y\;([x^2,y^2]=1)\) has the cardinality of the continuum.
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Structure of lattices of varieties and lattices of quasivarieties: Similarity and difference. I
Algebra and Logic, 1995The paper under review is the second part of the author's work which will be published in three parts [for the first part see Algebra Logika, 34, No. 2, 142-168 (1995); English translation: Algebra Logic 34, No. 2, 73-86 (1995; Zbl 0841.08005)]. The aim of the whole work is to provide a unified approach to the study of lattices of varieties and ...
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Coverings in the lattice of quasivarieties of groups
Siberian Mathematical Journal, 1987Let P be an infinite set of odd primes and M(P) the quasivariety of groups defined by quasi-identities \([x,y^ i,x]=1\to [x,y^ j,x]=1\) where i,j\(\in P\). Then M(P) has continuum covers in the lattice \(L_ q\) of quasivarieties of groups. There exist continuum quasivarieties of groups Q which have continuum covers in \(L_ q\) and satisfy any of the ...
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Coverings in the lattice of quasivarieties ofl-groups
Algebra and Logic, 1996We investigate the structure of the lattice of quasivarieties of lattice-ordered groups (l-groups). Series of coverings for certain particular quasivarieties of l-groups are constructed.
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