-универсальные квазимогообразия графов.
A characterization of quasivarieties of partial algebras by means of limits and products.
A unified syntactical approach to theorems of Putcha, Margolis, and Straubing on finite power semigroups.
Almost ff-universal and q-universal varieties of modular 0-lattices
A variety 𝕍 of algebras of a finite type is almost ff-universal if there is a finiteness-preserving faithful functor F: 𝔾 → 𝕍 from the category 𝔾 of all graphs and their compatible maps such that Fγ is nonconstant for every γ and every nonconstant homomorphism h: FG → FG' has the form h = Fγ for some γ: G → G'. A variety 𝕍 is Q-universal if its lattice of subquasivarieties has the lattice of subquasivarieties of any quasivariety of algebras of a finite type as the quotient of its sublattice....
An elementary proof that finite groups are projectively torsion-free
Classes of graphs definable by graph algebra identities or quasi-identities
Coverings in the lattice of quasivarieties of -groups.
Does imply axiom of choice?
E-free objects and E-locality for completely regular semigroups.
Embedding semigroups in groups. A geometrical approach.
Embedding sums of cancellative modes into semimodules
A mode (idempotent and entropic algebra) is a Lallement sum of its cancellative submodes over a normal band if it has a congruence with a normal band quotient and cancellative congruence classes. We show that such a sum embeds as a subreduct into a semimodule over a certain ring, and discuss some consequences of this fact. The result generalizes a similar earlier result of the authors proved in the case when the normal band is a semilattice.
Equations on the semidirect product of a finite semilattice by a finite commutative monoid.
Finite atomistic lattices that can be represented as lattices of quasivarieties
We prove that a finite atomistic lattice can be represented as a lattice of quasivarieties if and only if it is isomorphic to the lattice of all subsemilattices of a finite semilattice. This settles a conjecture that appeared in the context of [11].
Finitely generated almost universal varieties of -lattices
A concrete category is (algebraically) universal if any category of algebras has a full embedding into , and is almost universal if there is a class of -objects such that all non-constant homomorphisms between them form a universal category. The main result of this paper fully characterizes the finitely generated varieties of -lattices which are almost universal.
Finitely generated congruence distributive quasivarieties of algebras
Generalization of the concept of variety and quasivariety to partial algebras through category theory [Book]
Generalized varieties of commutative and nilpotent semigroups.
Homogeneous models and generic extensions.
Lattices of relative colour-families and antivarieties
We consider general properties of lattices of relative colour-families and antivarieties. Several results generalise the corresponding assertions about colour-families of undirected loopless graphs, see [1]. Conditions are indicated under which relative colour-families form a lattice. We prove that such a lattice is distributive. In the class of lattices of antivarieties of relation structures of finite signature, we distinguish the most complicated (universal) objects. Meet decompositions in lattices...
Monoid varieties defined by xn+1 = ... are local.