Completely Regular Semigroup Varieties

This book is a unified treatment of the most important core developments in the theoryof completely regular semigroup theory as it stands today. This volume focuses onthe lattice of varieties of completely regular semigroups. Since any in-depth study of thelattice of varieties requires an understanding of free completely regular semigroups, thebook begins by describing the free object on countably infinite sets and the propertiesof the lattice of fully invariant congruences on the free object. The authors introducevarious associated relations and operators on the lattice of varieties of completelyregular semigroups. Following that, the book covers the sublattice of varieties of bandswith a focus on the influence of that sublattice on the structure of the whole lattice.The book concludes with the remarkable theorem due to Polák describing the wholelattice of varieties of completely regular as a subdirect product of lattices,some ofwhich are well understood. The authors include recent advances, insights, results, andtechniques throughout the book.