The axiomatic rank of the quasivariety of orderable groups is infinite.
The cardinalities of the Green classes of the free objects in varieties of bands.
The category of connected partial unary algebras
The category of nonindexed algebras and weak homomorphisms
The category of recursive functions
The Chinese remainder theorem and sheaf representations
The class of algebras in which weak independence is equivalent to direct sums independence
The colimits in the generalized algebraic categories
The computability potential scale of all finite algebras.
The concept of structural regularity.
The congruence extension property for algebraic semigroups.
The congruence lattice of implication algebras.
The congruence variety of metabelian groups is not self-dual.
The Countable Chain Condition and Free Algebras.
The Csákány theory of regularity for finite algebras
The degrees of regularity in varieties
The dimension of a variety
Derived varieties were invented by P. Cohn in [4]. Derived varieties of a given type were invented by the authors in [10]. In the paper we deal with the derived variety of a given variety, by a fixed hypersubstitution σ. We introduce the notion of the dimension of a variety as the cardinality κ of the set of all proper derived varieties of V included in V. We examine dimensions of some varieties in the lattice of all varieties of a given type τ. Dimensions of varieties of lattices and all subvarieties...
The dual of the category of generalized trees.
The egg-box property of congruences
The epis of the category of ordered algebras and -continuous homomorphisms