The fundamental representation of a completely regular semigroup.
The fundamental representation of a regular semigroup.
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 generalized translational hull of a semigroup.
The Geometry of Self-adjunction
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 greatest Archimedean ideal in a semigroup
The greatest idempotent separating congruence on an ....-unipotent semigroup.
The group of units as a maximal inverse subsemigroup.
The groupoid of 0-reduced varieties of Semigroups (n).
The groupoid of varieties of idempotent semigroups.
The growth functions of finitely generated semigroups.
The hereditary pure monoids.
The homomorphic image of a T -semigroup.
The Hopf property and K-free products of semigroups.
The ideal structure of -semigroups
The injective hull of S-sets, S a semilattice of groups.
The intersection graph of a simply ordered semigroup.
The intersection of free submonoids of a free monoid is free.