Semihypergroup Theory

Semihypergroup Theory

1st Edition - June 2, 2016

Write a review

  • Author: Bijan Davvaz
  • Paperback ISBN: 9780128098158
  • eBook ISBN: 9780128099254

Purchase options

Purchase options
Available
DRM-free (Mobi, PDF, EPub)
Sales tax will be calculated at check-out

Institutional Subscription

Free Global Shipping
No minimum order

Description

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

Readership

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

Product details

  • No. of pages: 164
  • Language: English
  • Copyright: © Academic Press 2016
  • Published: June 2, 2016
  • Imprint: Academic Press
  • Paperback ISBN: 9780128098158
  • eBook ISBN: 9780128099254

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

Ratings and Reviews

Write a review

There are currently no reviews for "Semihypergroup Theory"