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Semihypergroup Theory - 1st Edition - ISBN: 9780128098158, 9780128099254

Semihypergroup Theory

1st Edition

Author: Bijan Davvaz
Paperback ISBN: 9780128098158
eBook ISBN: 9780128099254
Imprint: Academic Press
Published Date: 2nd June 2016
Page Count: 164
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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.

Key Features

  • 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

Table of Contents

  • 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


No. of pages:
© Academic Press 2016
2nd June 2016
Academic Press
Paperback ISBN:
eBook ISBN:

About the Author

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, Iran


"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

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