Results 211 to 220 of about 19,126 (247)

On the variety of strong subresiduated lattices

Mathematical Logic Quarterly, 2023
AbstractA subresiduated lattice is a pair , whereAis a bounded distributive lattice,Dis a bounded sublattice ofAand for every there exists the maximum of the set , which is denoted by . This pair can be regarded as an algebra of type (2, 2, 2, 0, 0), where . The class of subresiduated lattices is a variety which properly contains the variety of Heyting
Sergio A. Celani, Hernán Javier San Martín   +1 more
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LATTICES OF VARIETIES OF ALGEBRAS

Mathematics of the USSR-Sbornik, 1980
Let be an associative and commutative ring with 1, a subsemigroup of the multiplicative semigroup of , not containing divisors of zero, and some variety of -algebras. A study is made of the homomorphism from the lattice of all subvarieties of into the lattice of all varieties of -algebras, which is induced in a certain natural sense by the ...
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Varieties of Demi‐Pseudocomplemented Lattices

Mathematical Logic Quarterly, 1991
The authors present a solution to the problem of desribing the structure of the lattice of subvarieties of the variety of demi \(p\)-lattices, and in particular of almost \(p\)-lattices. The main purpose is to present an infinite poset \(P_ 0\) whose Hasse diagram is completely described by the following property: The lattice of subvarieties of the ...
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A Subsemilattice of the Lattice of Varieties of Lattice Ordered Groups

Canadian Journal of Mathematics, 1981
Each variety of lattice ordered groups determines a variety of groups, namely the variety of groups generated by the groups i n . In this paper a completely new and different correspondence between varieties of groups and varieties of lattice ordered groups is developed.
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Coverings in the lattice ofl-varieties

Algebra and Logic, 1983
A variety \(V\) of \(\ell\)-groups (\(\ell\)-variety) is said to be 0-approximable if \((x\wedge y^{-1}x^{-1}y)\vee e=e\) holds for every \(x,y\in G\) and \(G\in V\). The class \(L_0\) of all 0-approximable \(\ell\)-varieties is a lattice with respect to the naturally defined operations of sup and inf. Let \(\bar V, V\in L_0\).
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Splittings in the variety of residuated lattices

Algebra Universalis, 2000
A pair \(( {\mathcal V}_1, {\mathcal V}_2)\) of subvarieties of a variety \(\mathcal V\) is called a splitting pair if \({\mathcal V}_1 \not \subseteq {\mathcal V}_2\) and for any subvariety \(\mathcal S\) of \(\mathcal V\) either \({\mathcal V}_1 \subseteq \mathcal S\) or \({\mathcal S} \subseteq {\mathcal V}_2\). In such a case, \({\mathcal V}_1\) is
Kowalski, Tomasz, Ono, Hiroakira
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Varieties of lattice-ordered groups

Algebra and Logic, 1977
This is a clearly written survey article; it has the following sections: \(\ell\)-varieties; lattice ordered groups with subnormal jumps; subdirect products of linearly ordered groups; rigid lattice ordered groups; the lattice of \(\ell\)-varieties; the semigroup of \(\ell\)-varieties; free \(\ell\)-groups; the identity problem; radical classes.
Kopytov, V. M., Medvedev, N. Ya.
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Varieties of Lattices

2003
In this section, we shall discuss the basic properties of varieties of lattices. Of the four characterizations and descriptions given, three apply to arbitrary varieties of universal algebras; the fourth is valid only for those varieties of universal algebras that are congruence distributive (that is, the congruence lattice of any algebra in the ...
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On the Lattice of Varieties of Involution Semigroups

Semigroup Forum, 2001
A unary operator * on a semigroup \(S\) is called an involution if \(x^{**}=x\), \((xy)^*=y^*x^*\) for all \(x,y\in S\). Two sublattices of the lattice \(L({\mathcal S}^*)\) of varieties of involution semigroups are described, each generated by atoms of the lattice \(L({\mathcal S}^*)\). The first sublattice contains 18 elements and is generated by the
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Variety Invariants for Modular Lattices

Canadian Journal of Mathematics, 1969
A variety (primitive class) is a class of abstract algebras which is closed under the formation of subalgebras, homomorphic images, and products. For a given variety we shall call a function μ*, which assigns to each algebra a natural number or ∞, denoted by μ*(A), a variety invariant if for every natural number n the class of all with μ*(A) ≦ n is ...
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