Primitive classes of algebras with unary and nullary operations
Realization of small concrete categories by algebras and injective homomorphisms
The lattice of equational theories. Part II: The lattice of full sets of terms
Varieties of algebras with equationally definable zeros
The lattice of equational theories. Part III: Definability and automorphisms
The lattice of equational theories. Part I: Modular elements
The lattice of equational theories. Part IV: Equational theories of finite algebras
Principal dual ideals in lattices of primitive classes
Reduced dimension of primitive classes of universal algebras
Normal subsets of quasigroups
An embedding of groupoids and monomorphisms into simple groupoids
On atoms in lattices of primitive classes
The existence of upper semicomplements in lattices of primitive classes
Upper semicomplements and a definable element in the lattice of groupoid varieties
Enumerating left distributive groupoids
Varieties of idempotent slim groupoids
Idempotent slim groupoids are groupoids satisfying and . We prove that the variety of idempotent slim groupoids has uncountably many subvarieties. We find a four-element, inherently nonfinitely based idempotent slim groupoid; the variety generated by this groupoid has only finitely many subvarieties. We investigate free objects in some varieties of idempotent slim groupoids determined by permutational equations.
Three-variable equations of posets
We find an independent base for three-variable equations of posets.
Constructions over tournaments
We investigate tournaments that are projective in the variety that they generate, and free algebras over partial tournaments in that variety. We prove that the variety determined by three-variable equations of tournaments is not locally finite. We also construct infinitely many finite, pairwise incomparable simple tournaments.
Termal groupoids
We investigate the factor of the groupoid of terms through the largest congruence with a given set among its blocks. The set is supposed to be closed for overterms.
Slim groupoids
Slim groupoids are groupoids satisfying . We find all simple slim groupoids and all minimal varieties of slim groupoids. Every slim groupoid can be embedded into a subdirectly irreducible slim groupoid. The variety of slim groupoids has the finite embeddability property, so that the word problem is solvable. We introduce the notion of a strongly nonfinitely based slim groupoid (such groupoids are inherently nonfinitely based) and find all strongly nonfinitely based slim groupoids with at most four...
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