On definability in some lattices of semigroup varieties.

DOI10.1007/s00233-012-9429-8zbMath1273.20059OpenAlexW2001554928MaRDI QIDQ1939493

Olga Sapir, Grech, Mariusz

Publication date: 4 March 2013

Published in: Semigroup Forum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00233-012-9429-8

zbMATH Keywords

lattices of varietiespermutation identitiesfirst order definability0-reduced identitiesnil-varietiespermutative varieties

Mathematics Subject Classification ID

Lattices of varieties (08B15) Varieties and pseudovarieties of semigroups (20M07) Equational classes, universal algebra in model theory (03C05) Basic properties of first-order languages and structures (03C07)

Cites Work

• Proofs of definability of some varieties and sets of varieties of semigroups.
• Definability in the lattice of equational theories of semigroups
• Intervals in the lattice of varieties
• Modular and lower-modular elements of lattices of semigroup varieties.
• Precomplete varieties of semigroups
• Finitely generated permutative varieties.
• Lower-modular elements of the lattice of semigroup varieties.
• Bases for equational theories of semi-groups
• The lattice of semigroup varieties
• Semigroups satisfying permutation identities
• The structure and definability in the lattice of equational theories of strongly permutative semigroups
• Definability for equational theories of commutative groupoids
• The ordering of commutative terms
• Automorphisms of the lattice of equational theories of commutative semigroups
• The lattice of equational theories. Part II: The lattice of full sets of terms
• Definability in lattices of equational theoris
• Definability in the lattice of equational theories of commutative semigroups
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