Semihypergroup Theory
- 1st Edition - June 3, 2016
- Latest edition
- Author: Bijan Davvaz
- Language: English
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
"At present, the theory of semihypergroups is one of the most active fields of research in the area of hyperalgebraic structures. The book under review covers most of the mathematical ideas and techniques required in the study of semihypergroups. The book includes a number of topics, most of which reflect the author’s past research and thus provide a starting point for future research directions. Moreover, this is the first book presenting this theory."—MathSciNet
"This is the first book that specially introduces the concept of semihypergroup theory…The book exhaustively covers all concepts of semihypergroups and I believe that it could be a suitable reference for researchers."—Zentralblatt MATH
- Edition: 1
- Latest edition
- Published: June 3, 2016
- Language: English
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