Completely Regular Semigroup Varieties by Petrich, Mario; Reilly, Norman R.;

Applications and Advanced Techniques

Series: Synthesis Lectures on Mathematics & Statistics;

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Product details:

Edition number 2024
Publisher Springer
Date of Publication 5 February 2025
Number of Volumes 1 pieces, Book

ISBN 9783031488245
Binding Hardback
No. of pages198 pages
Size 240x168 mm
Language English
Illustrations 31 Illustrations, black & white

Short description:

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.

Long description:

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 is a 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.