On the characterization of primal partial algebras by strong regular hyperidentities.
On the conversion of binary algebras into semi-primal algebras
On the length of scales of computability potentials for -element algebras.
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, II
On the number of polynomials of a universal algebra, III
On traces of maximal clones.
On universal algebras having bases of different cardinalities
On varieties generated by Boolean clones.
On varieties of clones.
One interval in the lattice of partial hyperclones
In this paper the structure of the interval in the lattice of partial hyperclones is determined, where is the clone of all total operations and is the clone of all partial hyperoperations on .
One-generated clones of operations on binary relations
Order affine completeness of lattices with Boolean congruence lattices
This paper grew out from attempts to determine which modular lattices of finite height are locally order affine complete. A surprising discovery was that one can go quite far without assuming the modularity itself. The only thing which matters is that the congruence lattice is finite Boolean. The local order affine completeness problem of such lattices easily reduces to the case when is a subdirect product of two simple lattices and . Our main result claims that such a lattice is locally...
Orthorings
Certain ring-like structures, so-called orthorings, are introduced which are in a natural one-to-one correspondence with lattices with 0 every principal ideal of which is an ortholattice. This correspondence generalizes the well-known bijection between Boolean rings and Boolean algebras. It turns out that orthorings have nice congruence and ideal properties.