Completely Regular Semigroup Varieties: Applications and Advanced Techniques

ISBN-13: 9783031488245 / Angielski

Norman R. Reilly; Mario Petrich

Spis treści

General Sublattices of L(CR).- Neutrality and Intervals.- Free Objects.- Constructions.- Canonical Varieties.

O autorze

Mario Pettrich received his PhD from the University of Washington in 1961 and held positions in many universities across Austria, Canada, France, Germany, Italy, Portugal, Spain, the UK and the US, including Pennsylvania State University, University of Western Ontario, University of Vienna, University of St Andrews, Simon Fraser University, and University of Montpellier. He was a Founding Editor of Semigroup Forum. Dr. Petrich has published over 260 articles, seven monographs and one Research Note. The principal focus of his work was in the field of semigroup theory.

Norman Reilly received his PhD from Glasgow University in 1965 and has held positions at Glasgow University, Tulane University, and Simon Fraser University. Dr. Reilly has published over 100 articles and two books. He is a long time editor of Semigroup Forum and the International Journal of Algebra and Computation. The focus of his research has been on algebraic systems, including ordered algebraic systems, with a main focus on the theory of semigroups.

Blurb

This book presents further developments and applications in the area of completely regular semigroup theory. The authors begin by using a ladder technique to develop explicit descriptions of certain noteworthy sublattices of the lattice of varieties of completely regular semigroups. In particular, this book takes the first step towards expanding readers’ knowledge of the lattice at the very bottom, beyond, and somewhat parallel to the lattice of all varieties of bands. The book then takes advantage of the modularity of the lattice to derive subdirect product representations of certain ideals in terms of smaller better known varieties. The authors also devote two chapters to different aspects of free objects. The book ends with a fascinating conjecture regarding the sublattice of the lattice of varieties of completely regular semigroups generated by this family of largest elements.