Completely Regular Semigroup Varieties : A Comprehensive Study with Modern Insights (Synthesis Lectures on Mathematics & Statistics)

Petrich, Mario/ Reilly, Norman R.

Springer International Publishing AG（2025/03発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 238 p.
• 言語 ENG
• 商品コード 9783031428937
• DDC分類 512.27

Full Description

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.

Contents

Fully Invariant Relations.- Kernel and Trace Relations.- Bands.- Polák Theorem.