On the lattice of varieties of completely simple semigroups.
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 one principal congruence identity
On the Pin-Thérien expansion of idempotent monoids.
On the quasivarieties generated by finite semigroups.
On the relation between heterogeneous uniform 2-algebraic closure operators and heterogeneous algebras.
On the relationship between projective distributive lattices and Boolean algebras.
On the ring of the variety of algebras over a ring
On the solidity of general varieties of tree languages
For a class of hypersubstitutions 𝓚, we define the 𝓚-solidity of general varieties of tree languages (GVTLs) that contain tree languages over all alphabets, general varieties of finite algebras (GVFAs), and general varieties of finite congruences (GVFCs). We show that if 𝓚 is a so-called category of substitutions, a GVTL is 𝓚-solid exactly in case the corresponding GVFA, or the corresponding GVFC, is 𝓚-solid. We establish the solidity status of several known GVTLs with respect to certain categories...
On the Specht property of varieties of commutative alternative algebras over a field of characteristic 3 and commutative Moufang loops.
On the structure of equationally complete varieties. I
On the structure of semilattice sums
On the varieties of Cliffordian Semigroups.
On the varieties of completely regular semigroups.
On two classes of hereditarily finitely based semigroup identities.
On universality of semigroup varieties
A category is called -determined if every set of non-isomorphic -objects such that their endomorphism monoids are isomorphic has a cardinality less than . A quasivariety is called -universal if the lattice of all subquasivarieties of any quasivariety of finite type is a homomorphic image of a sublattice of the lattice of all subquasivarieties of . We say that a variety is var-relatively alg-universal if there exists a proper subvariety of such that homomorphisms of whose image does...
On varieties generated by Boolean clones.
On varieties of clones.
On varieties of combinatorial inverse semigroups I.
On varieties of combinatorial inverse semigroups II.