Semihypergroup Theory
- 1st Edition - June 3, 2016
- Latest edition
- Author: Bijan Davvaz
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 8 0 9 8 1 5 - 8
- eBook ISBN:9 7 8 - 0 - 1 2 - 8 0 9 9 2 5 - 4
Semihypergroup Theory is the first book devoted to the semihypergroup theory and it includes basic results concerning semigroup theory and algebraic hyperstructures, which rep… Read more
Semihypergroup Theory is the first book devoted to the semihypergroup theory and it includes basic results concerning semigroup theory and algebraic hyperstructures, which represent the most general algebraic context in which reality can be modelled.
Hyperstructures represent a natural extension of classical algebraic structures and they were introduced in 1934 by the French mathematician Marty. Since then, hundreds of papers have been published on this subject.
- Offers the first book devoted to the semihypergroup theory
- Presents an introduction to recent progress in the theory of semihypergroups
- Covers most of the mathematical ideas and techniques required in the study of semihypergroups
- Employs the notion of fundamental relations to connect semihypergroups to semigroups
Theoreticians in pure and applied mathematics
- Preface
- Chapter 1: A Brief Excursion Into Semigroup Theory
- Abstract
- 1.1 Basic Definitions and Examples
- 1.2 Divisibility of Elements
- 1.3 Regular and Inverse Semigroups
- 1.4 Subsemigroups, Ideals, Bi-Ideals, and Quasi-Ideals
- 1.5 Homomorphisms
- 1.6 Congruence Relations and Isomorphism Theorems
- 1.7 Green’s Relations
- 1.8 Free Semigroups
- 1.9 Approximations in a Semigroup
- 1.10 Ordered Semigroups
- Chapter 2: Semihypergroups
- Abstract
- 2.1 History of Algebraic Hyperstructures
- 2.2 Semihypergroup and Examples
- 2.3 Regular Semihypergroups
- 2.4 Subsemihypergroups and Hyperideals
- 2.5 Quasi-Hyperideals
- 2.6 Prime and Semiprime Hyperideals
- 2.7 Semihypergroup Homomorphisms
- 2.8 Regular and Strongly Regular Relations
- 2.9 Simple Semihypergroups
- 2.10 Cyclic Semihypergroups
- Chapter 3: Ordered Semihypergroups
- Abstract
- 3.1 Basic Definitions and Examples
- 3.2 Prime Hyperideals of the Cartesian Product of Two Ordered Semihypergroups
- 3.3 Right Simple Ordered Semihypergroups
- 3.4 Ordered Semigroups (Semihypergroups) Derived From Ordered Semihypergroups
- Chapter 4: Fundamental Relations
- Abstract
- 4.1 The β Relation
- 4.2 Complete Parts
- 4.3 The Transitivity of the Relation β in Semihypergroups
- 4.4 The α Relation
- Chapter 5: Conclusion
- Bibliography
- Index
- Edition: 1
- Latest edition
- Published: June 3, 2016
- Language: English
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Bijan Davvaz
Professor Bijan Davvaz took his B.Sc. degree in Applied Mathematics at Shiraz University, Iran in 1988 and his M.Sc. degree in Pure Mathematics at Tehran University in 1990. In 1998, he received his Ph.D. in Mathematics at TarbiatModarres University. He is a member of Editorial Boards of 20 Mathematical journals. He is author of around 350 research papers, especially on algebraic hyperstructures and their applications. Moreover, he published five books in algebra. He is currently Professor of Mathematics at Yazd University in Iran.
Affiliations and expertise
Department of Mathematics, Yazd University, Yazd, IranRead Semihypergroup Theory on ScienceDirect