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Directoids: algebraic models of up-directed sets
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Definability in the lattice of equational theories of semigroups
We study first-order definability in the latticeL of equational theories of semigroups. A large collection of individual theories and some interesting sets of theories are definable inL. As examples,…
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Definability in Substructure Orderings, II: Finite Ordered Sets
TLDR
It is shown that every isomorphism-invariant relation between finite posets that is definable in a certain strongly enriched second-order language is first-order definable up to duality in the ordered set p.
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Equational theories of medial groupoids
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Intervals in the lattice of varieties
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Free commutative idempotent abelian groupoids and quasigroups
Primitive classes of algebras with unary and nullary operations
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The lattice of varieties of commutative abelian distributive groupoids
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Finitely generated algebraic structures with various divisibility conditions
Abstract. Infinite fields are not finitely generated rings. A similar question is considered for further algebraic structures, mainly commutative semirings. In this case, purely algebraic methods…
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Subdirectly irreducible semilattices with an automorphism
In other words, SA is the variety of semilattices with one automorphism (which is, as well as its inverse, considered as an additional fundamental operation). The aim of this paper is to find all…
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