Results 231 to 240 of about 165,943,886 (264)

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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Quasiorder lattices of varieties [PDF]

Algebra universalis, 2018
The set \(\mathrm{Quo}(A)\) of compatible quasiorders of an algebra \(A\) forms a lattice under inclusion and the congruence lattice \(\mathrm{Con}(A)\) is its sublattice. It is proved that a locally finite variety is congruence distributive (modular) if and only if it is quasiorder distributive (modular).
Gyenizse Gergő, Maróti Miklós
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LATTICES OF VARIETIES OF LINEAR ALGEBRAS

Russian Mathematical Surveys, 1978
ContentsIntroduction § 1. Varieties of linear algebras § 2. Residually nilpotent chain varieties of algebras § 3. Precomplete varieties of algebras § 4. Chain varieties of alternative, right alternative Lie-admissible, and Jordan algebras § 5. Chain varieties of restricted Lie p-algebras § 6.
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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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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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Minimal Varieties of Involutive Residuated Lattices

Studia Logica, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Constantine Tsinakis, Annika M. Wille
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Complete Congruences on Lattices of Varieties and of Pseudovarieties

International Journal of Algebra and Computation, 1998
Three methods for the construction of all complete congruences on the lattice Lv( V ) of subvarieties of a variety V are introduced. It is shown that there exists an order preserving embedding of the lattice of complete congruences on the lattice Lp( P ) of all subpseudovarieties of a given pseudovariety P into the direct product of the lattices of ...
Francis Pastijn, Peter G. Trotter
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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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Embedding lattices in lattices of varieties of groups

Izvestiya: Mathematics, 1999
Let \(\Lambda\) denote the direct product of subspace lattices, one for each finite-dimensional vector space over the \(2\)-element field, and let \(\mathbb{A}_2\) be the group variety defined by the law \(x^2=1\). The main result of the paper is that \(\Lambda\) embeds in the interval \([\mathbb{A}_2^4,\mathbb{A}_2^5]\) of the lattice of group ...
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