The ascending varietal chain of a variety of semigroups.
The bifree regular E-solid semigroups.
The cardinalities of the Green classes of the free objects in varieties of bands.
The concept of structural regularity.
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 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 algebra in the variety generated by quasi-trivial semigroups
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 globals of pseudovarieties of ordered semigroups containing and an application to a problem proposed by Pin
Given a basis of pseudoidentities for a pseudovariety of ordered semigroups containing the 5-element aperiodic Brandt semigroup , under the natural order, it is shown that the same basis, over the most general graph over which it can be read, defines the global. This is used to show that the global of the pseudovariety of level of Straubing-Thérien’s concatenation hierarchy has infinite vertex rank.
The globals of pseudovarieties of ordered semigroups containing B2 and an application to a problem proposed by Pin
Given a basis of pseudoidentities for a pseudovariety of ordered semigroups containing the 5-element aperiodic Brandt semigroup B2, under the natural order, it is shown that the same basis, over the most general graph over which it can be read, defines the global. This is used to show that the global of the pseudovariety of level 3/2 of Straubing-Thérien's concatenation hierarchy has infinite vertex rank.
The groupoid of 0-reduced varieties of Semigroups (n).
The hereditary pure monoids.
The Hopf property and K-free products of semigroups.
The join of the pseudovarieties of idempotent semigroups and locally trivial semigroups.
The lattice of semigroup varieties.
The lattice of varieties and pseudovarieties of band monoids.
The lattice of varieties of *-regular band monoids.
The local and global varieties induced by nilpotent monoids