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Completely Regular Semigroup Varieties: Synthesis Lectures on Mathematics & Statistics

Autor Mario Petrich, Norman R. Reilly
en Limba Engleză Paperback – 13 mar 2025
Since any in-depth study of the lattice of varieties requires an understanding of free completely regular semigroups, the book begins by describing the free object on countably infinite sets and the properties of the lattice of fully invariant congruences on the free object.
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Specificații

ISBN-13: 9783031428937
ISBN-10: 3031428935
Pagini: 252
Dimensiuni: 168 x 240 x 14 mm
Greutate: 0.43 kg
Editura: Springer
Seria Synthesis Lectures on Mathematics & Statistics


Cuprins

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

Notă biografică

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, witha main focus on the theory of semigroups.

Textul de pe ultima copertă

This book presents further developments and applications in the area of completely regular semigroup theory, beginning with applications of Polák’s theorem to obtain detailed descriptions of various kernel classes including the K-class covers of the kernel class of all bands.  The important property of modularity of the  lattice of varieties of completely regular semigroups is then employed to analyse various principal sublattices.  This is followed by a study of certain important complete congruences on the lattice; the group, local and core relations.  The next chapter is devoted to a further treatment of certain free objects and related word problems.  There are many constructions in the theory of semigroups.  Those that have played an important role in the theory of varieties of completely regular semigroups are presented as they apply in this context.  The mapping that takes each variety to its intersection with the variety of bands isa complete retraction of the lattice of varieties of completely regular semigroups onto the lattice of band varieties and so induces a complete congruence for which every class has a greatest member.  The sublattice generated by these greatest members is then investigated with the help of many applications of Polák’s theorem. The book closes with a fascinating conjecture regarding the structure of this sublattice.

Caracteristici

Includes recent advances, insights, results, and techniques throughout the book in order to expand on the topic Introduces various relations and operators on the lattice of varieties of completely regular semigroups Provides background on free completely regular semigroups to ensure that readers understand the basic concepts