Terms and semiterms
The ascending varietal chain of a variety of semigroups.
The cardinalities of the Green classes of the free objects in varieties of bands.
The class of algebras in which weak independence is equivalent to direct sums independence
The congruence lattice of implication algebras.
The congruence variety of metabelian groups is not self-dual.
The Countable Chain Condition and Free 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 egg-box property of congruences
The equational theory of paramedial cancellation groupoids
The existence of upper semicomplements in lattices of primitive classes
The finite basis problem in the pseudovariety joins of aperiodic semigroups with groups.
The finite basis question for semigroups of order less than six.
The finiteness of a base of indentities for fiveelement monoids
The free one-generated left distributive algebra: basics and a simplified proof of the division algorithm
The left distributive law is the law a· (b· c) = (a·b) · (a· c). Left distributive algebras have been classically used in the study of knots and braids, and more recently free left distributive algebras have been studied in connection with large cardinal axioms in set theory. We provide a survey of results on the free left distributive algebra on one generator, A, and a new, simplified proof of the existence of a normal form for terms in A. Topics included are: the confluence of A, the linearity...
The Galois correspondence between subvariety lattices and monoids of hpersubstitutions
Denecke and Reichel have described a method of studying the lattice of all varieties of a given type by using monoids of hypersubstitutions. In this paper we develop a Galois correspondence between monoids of hypersubstitutions of a given type and lattices of subvarieties of a given variety of that type. We then apply the results obtained to the lattice of varieties of bands (idempotent semigroups), and study the complete sublattices of this lattice obtained through the Galois correspondence.
The groupoid of 0-reduced varieties of Semigroups (n).
The hereditary pure monoids.
The join of the pseudovarieties of idempotent semigroups and locally trivial semigroups.