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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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Varieties of lattices

1988
An interesting problem in universal algebra is the connection between the internal structure of an algebra and the identities which it satisfies. The study of varieties of algebras provides some insight into this problem. Here we are concerned mainly with lattice varieties, about which a wealth of information has been obtained in the last twenty years.
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The lattice of varieties of monoids

Japanese Journal of Mathematics, 2022
Sergey Gusev, Edmond W H Lee
exaly