On the arity of affine modules
On the associative Nijenhuis relation.
On the characterisation of Mal'tsev and Jónsson-Tarski algebras
There are very strong parallels between the properties of Mal'tsev and Jónsson-Tarski algebras, for example in the good behaviour of centrality and in the factorization of direct products. Moreover, the two classes between them include the majority of algebras that actually arise 'in nature'. As a contribution to the research programme building a unified theory capable of covering the two classes, along with other instances of good centrality and factorization, the paper presents a common framework...
On the congruence extension property.
On the degrees of permutability of subregular varieties
On the dual space of an MS-algebra.
On the existence of non-trivial tolerances in permutable algebras
On the failure of Birkhoff's theorem for locally small based equational categories of algebras
On the finite basis property for semigroup varieties.
On the lattice of completely regular monoid varieties.
On the lattice of torsion classes of lattice ordered groups
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...