The book presents an updated study of hypergroups, being structured on 12 chapters in starting with the presentation of the basic notions in the domain: semihypergroups, hypergroups, classes of subhypergroups, types of homomorphisms, but also key notions: canonical hypergroups, join spaces and complete hypergroups. A detailed study is dedicated to the connections between hypergroups and binary relations, starting from connections established by Rosenberg and Corsini. Various types of binary relations are highlighted, in particular equivalence relations and the corresponding quotient structures, which enjoy certain properties: commutativity, cyclicity, solvability.A special attention is paid to the fundamental beta relationship, which leads to a group quotient structure. In the finite case, the number of non-isomorphic Rosenberg hypergroups of small orders is mentioned. Also, the study of hypergroups associated with relations is extended to the case of hypergroups associated to n-ary relations. Then follows an applied excursion of hypergroups in important chapters in mathematics: lattices, Pawlak approximation, hypergraphs, topology, with various properties, characterizations, varied and interesting examples. The bibliography presented is an updated one in the field, followed by an index of the notions presented in the book, useful in its study.
Contents:
- Preface
- Semihypergroups
- Hypergroups
- Subhypergroups
- Homomorphisms and Isomorphisms
- Fundamental Relations
- More about the Corresponding Quotient Structures
- Join Spaces, Canonical Hypergroups and Lattices
- Rosenberg Hypergroups
- Hypergroups and n-ary Relations
- Approximations in Hypergroups
- Links between Hypergraphs and Hypergroups
- Topological Hypergroups
- Bibliography
- Index
Readership: Advanced undergraduate and graduate students, researchers and practitioners in the fields of algebra, group theory and algebraic hyperstructures.
Key Features:
- The authors of the book are expert and well known on this theory. So, mostresults on hypergroups are collected in this book
- The overall aim of the book is to present an introduction to some of the results, methods and ideas about hypergroups
- The relationships between large groups and other branches of mathematics such as topology, graph theory, combinatorics, and approximation theory are discussed
