A01=Bijan Davvaz
A01=Violeta Leoreanu-fotea
Abelian Group
Author_Bijan Davvaz
Author_Violeta Leoreanu-fotea
Binary Relation
Canonical Hypergroup
Category=PBG
Complete Hypergroup
Complete Part
Cyclic Group
Direct Hyperproduct
Direct Product
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Euler's Totient Function
Extension of Canonical Hypergroup by Canonical Hypergroup
Fundamental Group
Fundamental Relation
Homomorphism
Hypergraph
Hypergroup
Hypergroupoid
Hyperoperation
Isomorphism
Join Space
Lattice
Lower Approximation
Multisemi-Direct Hyperproduct
N-ary Relation
Neighborhood Operator
Reduced Hypergroup
Regular Relation
Rosenberg Hypergroup
Rough Subhypergroup
Semihypergroup
Solvable Group
Strongly Regular Relation
Subhypergroup
Topological Hypergroup
Topological Hypergroupoid
Topological Space
Upper Approximation
Weak Mutually Associativity
Product details
- ISBN 9789811249389
- Publication Date: 10 Feb 2022
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
