Results 51 to 60 of about 439 (93)

The structure of the lattices of quasivarieties

Algebra Universalis, 1994
For an algebraic system \(A\) and a quasivariety \(\mathcal K\) let \(\text{Con}_{{\mathcal K}} A\) be the lattice of all congruence relations \(\theta\) on \(A\) such that \(A/\theta\in {\mathcal K}\). Define the embedding relation \(\leq\) as follows: \(\theta\leq \theta'\) iff \(A/\theta'\) is embeddable into \(A/\theta\).
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The Lattice of Quasivarieties of Torsion-Free Metabelian Groups

Algebra and Logic, 2003
Let \(M\) be a quasivariety and let \(L_q(M)\) be the lattice of quasivarieties in \(M\). The author denotes by \(F_2(A^2)\) a free metabelian group on two generators and by \(F_2(N_2)\) a free nilpotent group of degree two on two generators. Theorem 2.
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Complexity of quasivariety lattices for varieties of differential groupoids. II

Siberian Advances in Mathematics, 2009
Summary: 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, 1989
See the review in Zbl 0656.20032.
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A Lattice of Quasivarieties of Normal Cryptogroups

Semigroup Forum, 2007
A 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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Quasivarieties and Varieties of Lattice-Ordered Groups

1996
Many properties and statements of the theory of lattice-ordered groups (l-groups) can be formulated and proved in terms of first order logic. Special mention should be made of properties expressed by universal sentences such as identities and implications, which can be referred to as the theory of varieties and quasivarieties, respectively, of l-groups.
V. M. Kopytov, N. Ya. Medvedev
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On coatoms in lattices of quasivarieties of algebraic systems

algebra universalis, 2001
Let \(qK\) 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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On atoms in the lattice of quasivarieties

Algebra Universalis, 1987
A 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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The lattice of quasivarieties of metabelian groups

Algebra and Logic, 1996
The 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, 1995
The 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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