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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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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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Quasiorder lattices of varieties
Algebra universalis, 2018The 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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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.
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Semisimples in Varieties of Commutative Integral Bounded Residuated Lattices
Studia Logica, 2016Antoni Torrens
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The Failure of The Amalgamation Property for Semilinear Varieties of Residuated Lattices
Mathematica Slovaca, 2015José Gil-Férez +2 more
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