Results 41 to 50 of about 101 (90)

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,
M. E. Adams, Wieslaw Dziobiak
openaire   +2 more sources

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 ...
openaire   +2 more sources

On quasivarieties and varieties as categories

Studia Logica, 2004
The 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
openaire   +1 more source

SUBFUNCTORS ASSOCIATED WITH QUASIVARIETIES

1984
Quasivarieties of algebras are characterized as SP-classes closed under a certain construction of directed unions of congruences.
openaire   +2 more sources

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.
openaire   +2 more sources

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 ...
openaire   +2 more sources

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 ...
openaire   +2 more sources

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.
openaire   +2 more sources

On the lattice of quasivarieties of Sugihara algebras

Studia Logica, 1986
A 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
openaire   +2 more sources

Quasivarieties of Graphs and Independent Axiomatizability

Siberian Advances in Mathematics, 2018
Summary: 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.
openaire   +1 more source