On the lattice of varieties of completely simple semigroups.
On the lattices of quasivarieties of differential groupoids
The main result of Romanowska A., Roszkowska B., On some groupoid modes, Demonstratio Math. 20 (1987), no. 1–2, 277–290, provides us with an explicit description of the lattice of varieties of differential groupoids. In the present article, we show that this variety is -universal, which means that there is no convenient explicit description for the lattice of quasivarieties of differential groupoids. We also find an example of a subvariety of differential groupoids with a finite number of subquasivarieties....
On the length of scales of computability potentials for -element algebras.
On the membership problem for pseudo-varieties of commutative semigroups.
On the nontrivial solvability of systems of homogeneous linear equations over in ZFC
Motivated by the paper by H. Herrlich, E. Tachtsis (2017) we investigate in ZFC the following compactness question: for which uncountable cardinals , an arbitrary nonempty system of homogeneous -linear equations is nontrivially solvable in provided that each of its subsystems of cardinality less than is nontrivially solvable in ?
On the number of closed subsets of linear functions in the 6-valued logic
On the number of finite algebraic structures
We prove that every clone of operations on a finite set , if it contains a Malcev operation, is finitely related – i.e., identical with the clone of all operations respecting for some finitary relation over . It follows that for a fixed finite set , the set of all such Malcev clones is countable. This completes the solution of a problem that was first formulated in 1980, or earlier: how many Malcev clones can finite sets support? More generally, we prove that every finite algebra with few...
On the number of polynomials of a universal algebra, I
On the number of polynomials of a universal algebra, II
On the number of polynomials of a universal algebra, III
On the number of polynomials of a universal algebra, IV
On the one principal congruence identity
On the partial semi-hypergroups with empty diagonal
On the Pin-Thérien expansion of idempotent monoids.
On the power semigroup of a finite semigroup
On the quasivarieties generated by finite semigroups.
On the Quotient (omega,m)-ringoids
On the quotient ( ,m)-ringoids.
On the reconstruction of Boolean algebras from their automorphism groups.
On the relation between heterogeneous uniform 2-algebraic closure operators and heterogeneous algebras.