Results 31 to 40 of about 74 (68)

ASSERTIONALLY EQUIVALENT QUASIVARIETIES

International Journal of Algebra and Computation, 2008
A translation in an algebraic signature is a finite conjunction of equations in one variable. On a quasivariety K, a translation τ naturally induces a deductive system, called the τ-assertional logic of K. Two quasivarieties are τ-assertionally equivalent if they have the same τ-assertional logic. This paper is a study of assertional equivalence.
Blok, W. J., Raftery, J. G.
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QUASIVARIETIES OF IDEMPOTENT SEMIGROUPS

International Journal of Algebra and Computation, 2003
It is proved that the lattice L(Bd) of quasivarieties contained in the variety Bdof idempotent semigroups contains an isomorphic copy of the ideal lattice of a free lattice on ω free generators. This result shows that a problem of Petrich [19], which calls for a description of L(Bd), is much more complex than originally expected.
Adams, M. E., Dziobiak, W.
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Complexity of Quasivariety Lattices

Algebra and Logic, 2015
A 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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Levi quasivarieties

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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Q-Universal Quasivarieties of Algebras

Proceedings of the American Mathematical Society, 1994
For any quasivariety \({\mathbf K}\) of algebras (of finite type), let \(L({\mathbf K})\) be the lattice of all quasivarieties in \({\mathbf K}\). Call \({\mathbf K}\) \(Q\)-universal iff for any quasivariety \({\mathbf M}\) (of algebras of finite type), \(L({\mathbf M})\) is a homomorphic image of a sublattice of \(L({\mathbf K})\).
Adams, M. E., Dziobiak, W.
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UNREASONABLE LATTICES OF QUASIVARIETIES

International Journal of Algebra and Computation, 2012
A 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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Quasivarieties of Metric Algebras

Algebra and Logic, 2003
The 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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Joins of minimal quasivarieties

Studia Logica, 1995
Let \({\mathcal D}_2\) denote the variety of algebras \((L;\wedge, \vee, 0, c_0, c_1,1)\) which are distributive \((0,1)\)-lattices with two distinguished elements \(c_0, c_1\in L\). It is known that the only subdirectly irreducible algebras in \({\mathcal D}_2\) are \(2_{ij}= (\{0, 1\};\wedge, \vee, 0, i,j, 1)\) with \(i,j\in \{0, 1\}\). Let, further,
Adams, M. E., Dziobiak, W.
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Quasivarieties of Cantor algebras

Algebra Universalis, 2001
A 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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Quasivarieties of distributivep-algebras

Algebra Universalis, 1992
The paper exhibits three results on quasivarieties of (distributive) \(p\)- algebras: There exists a quasivariety \(\mathbb{K}\) of such algebras such that \(\mathbb{B}_ 2\subset\mathbb{K}\subset\mathbb{B}_ 4\), but neither \(\mathbb{K}\subseteq\mathbb{B}_ 3\) nor \(\mathbb{B}_ 3\subseteq\mathbb{K}\), where \(\mathbb{B}_ i\) denotes the \(i\)-th Lee ...
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