On the homology theory of categories. II.
On the join of equational classes of idempotent algebras and algebras with constants
On the lattice of congruences on inverse semirings
Let S be a semiring whose additive reduct (S,+) is an inverse semigroup. The relations θ and k, induced by tr and ker (resp.), are congruences on the lattice C(S) of all congruences on S. For ρ ∈ C(S), we have introduced four congruences and on S and showed that and . Different properties of ρθ and ρκ have been considered here. A congruence ρ on S is a Clifford congruence if and only if is a distributive lattice congruence and is a skew-ring congruence on S. If η (σ) is the least distributive...
On the lattice of convex subsets of a partial monounary algebra
On the length of scales of computability potentials for -element algebras.
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 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.
On the representation of lattices by subsemigroup lattices of bands.
On the semigroup structure of cyclic left distributive algebras.