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Hoop Algebras : An Introduction / by Anatolij Dvurečenskij, Omid Zahiri, Mona Aaly Kologani, Rajab Ali Borzooei.
Springer Nature - Springer Mathematics and Statistics (R0) eBooks 2026 English International Available online
View online- Format:
- Book
- Author/Creator:
- Dvurečenskij, Anatolij.
- Series:
- Frontiers in Mathematics, 1660-8054
- Language:
- English
- Subjects (All):
- Algebra.
- Algebra, Universal.
- Order, Lattices, Ordered Algebraic Structures.
- General Algebraic Systems.
- Local Subjects:
- Order, Lattices, Ordered Algebraic Structures.
- General Algebraic Systems.
- Physical Description:
- 1 online resource (747 pages)
- Edition:
- 1st ed. 2026.
- Place of Publication:
- Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2026.
- Summary:
- 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.
- 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.
- Notes:
- Description based on publisher supplied metadata and other sources.
- ISBN:
- 3-032-11736-4
- 9783032117366
- OCLC:
- 1581074406
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