フープ代数入門 Hoop Algebras : An Introduction

著者名：Dvurečenskij, Anatolij/Zahiri, Omid/Aaly Kologani, Mona/Borzooei, Rajab Ali

Birkhäuser（2026/02/20発売）

• 言語：ENG
• ISBN：9783032117359
• eISBN：9783032117366

Description

This book offers a comprehensive and in-depth exploration of hoop theory, a fascinating branch of algebra with deep connections to logic and other areas of mathematics. Among algebraic structures, hoops stand out as a rich subject of study, bridging the worlds of residuated lattices, BL-algebras, MV-algebras, and related systems.

 

Starting with fundamental concepts of algebraic and lattice-theoretical structures, the book gradually delves into the core theory of hoops, investigating their algebraic structure, properties, and relationships with other algebraic systems. Significant attention is also devoted to the lattice-theoretical properties of hoops, and the interplay between algebraic and logical perspectives is emphasized.
  
This book is intended for advanced undergraduates with a background in algebra and logic, Ph.D. students, and researchers. Featuring a number of examples and exercises, it serves as a valuable resource for those seeking a comprehensive and in-depth understanding of hoop theory and its applications.

Table of Contents

Chapter 1. Basic notions.- Chapter 2. Pocrims and Related Structures.- Chapter 3. Structure of hoops.- Chapter 4. Filters and congruences of hoops.- Chapter 5. Algebraic structures related to hoops.- Chapter 6. Lattice-theoretical properties.- Chapter 7. State hoops.- Chapter 8. Appendix A - A trip into non-commutative structures.- Chapter 9. Appendix B.