Completely Regular Semigroup Varieties : A Comprehensive Study with Modern Insights

Norman R. Reilly

ISBN 10: 3031428900 / ISBN 13: 9783031428906

Published by Springer Nature Switzerland, 2024

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783031428906

Bibliographic Details

• Title: Completely Regular Semigroup Varieties : A Comprehensive Study with Modern Insights
• Publisher: Springer Nature Switzerland
• Publication Date: 2024
• Language: English
• ISBN 10: 3031428900
• ISBN 13: 9783031428906
• Binding: Buch
• Condition: Neu
• Dimensions: 246W x 173H x 20D millimeters 246 millimeters width by 173 millimeters height by 20 millimeters depth
• Weight: 605 grams

About this title

Synopsis

This book is a unified treatment of the most important core developments in the theory of completely regular semigroup theory as it stands today. This volume focuses on the lattice of varieties of completely regular semigroups. 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. The authors introduce various associated relations and operators on the lattice of varieties of completely regular semigroups. Following that, the book covers the sublattice of varieties of bands with 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 whole lattice of varieties of completely regular as a subdirect product of lattices,some of which are well understood. The authors include recent advances, insights, results, and techniques throughout the book.

About the Author

Mario Petrich received his Ph.D. 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.

Norman Reilly received his Ph.D. 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.