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Varieties of lattice-ordered groups
Algebra and Logic, 1977This 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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Variety Invariants for Modular Lattices
Canadian Journal of Mathematics, 1969A 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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On the Lattice of Varieties of Involution Semigroups
Semigroup Forum, 2001A 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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Minimal Varieties of Involutive Residuated Lattices
Studia Logica, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Constantine Tsinakis, Annika M. Wille
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LATTICES OF VARIETIES OF LINEAR ALGEBRAS
Russian Mathematical Surveys, 1978ContentsIntroduction § 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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Complete Congruences on Lattices of Varieties and of Pseudovarieties
International Journal of Algebra and Computation, 1998Three 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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Algebra Universalis, 1985
The concept of variety product originated in \textit{H. Neumann}'s work on ''Varieties of groups'' [Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 37 (1967; Zbl 0251.20001)] and was generalized to universal algebra by \textit{A. I. Mal'cev} [Sib. Mat. Zh.
Grätzer, George, Kelly, David
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The concept of variety product originated in \textit{H. Neumann}'s work on ''Varieties of groups'' [Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 37 (1967; Zbl 0251.20001)] and was generalized to universal algebra by \textit{A. I. Mal'cev} [Sib. Mat. Zh.
Grätzer, George, Kelly, David
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Embedding lattices in lattices of varieties of groups
Izvestiya: Mathematics, 1999Let \(\Lambda\) 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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2015
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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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.
openaire +1 more source