Some Properties of Hypermodules Over Krasner Hyperrings PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Some Properties of Hypermodules Over Krasner Hyperrings PDF full book. Access full book title Some Properties of Hypermodules Over Krasner Hyperrings by . Download full books in PDF and EPUB format.
Author:
Publisher:
ISBN:
Category : Hypergroups
Languages : en
Pages : 174
Get Book Here
Book Description
A system (R,+,.) is said to be a Krasner hyperring if (i) (R,+) is a canonical hypergroup, (ii) (R,.) is a semigroup with zero 0 where 0 is the scalar identity of (R,+) and (iii) x.(y+z)=x.y+x.z and (y+z).x=y.x+z.x for all x,y,z [is an element of a set] R. A hypermodule over a Krasner hyperring R is a canonical hypergroup M, for which there is a function (r,m) [right arrow]rm from RxM into M such that for all r, r[subscript 1], r[subscript 2] [is an element of a set]R and m, m[subscript 1],m[subacript 2] [is an element of a set] M, (i) r(m[subscript 1]+m[subscript 2])=rm[subscript 1]+rm[subscript 2], (ii) )(r[subscript 1]+r[subscript 2])m=r[subscript 1]m+r[subscript 2]m , (iii) (r[subscript 1].r[subscript 2])m=r[subscript 1](r[subscript 2]m) and (iv) 0[subscript r]m=0[subscript M]. In this research, various elementary properties of modules over rings are generalized to properties of hypermodules over Krasner hyperrings and some concrete examples of hypermodules over Krasner hyperrings are given by considering among the collection of all multiplicative interval semigroups joining 0 on the system of real numbers and some hyperoperations. Moreover, we give a definition of projective hypermodule which is parallel to the definition of projective module in module theory and study some related properties.
Author:
Publisher:
ISBN:
Category : Hypergroups
Languages : en
Pages : 174
Get Book Here
Book Description
A system (R,+,.) is said to be a Krasner hyperring if (i) (R,+) is a canonical hypergroup, (ii) (R,.) is a semigroup with zero 0 where 0 is the scalar identity of (R,+) and (iii) x.(y+z)=x.y+x.z and (y+z).x=y.x+z.x for all x,y,z [is an element of a set] R. A hypermodule over a Krasner hyperring R is a canonical hypergroup M, for which there is a function (r,m) [right arrow]rm from RxM into M such that for all r, r[subscript 1], r[subscript 2] [is an element of a set]R and m, m[subscript 1],m[subacript 2] [is an element of a set] M, (i) r(m[subscript 1]+m[subscript 2])=rm[subscript 1]+rm[subscript 2], (ii) )(r[subscript 1]+r[subscript 2])m=r[subscript 1]m+r[subscript 2]m , (iii) (r[subscript 1].r[subscript 2])m=r[subscript 1](r[subscript 2]m) and (iv) 0[subscript r]m=0[subscript M]. In this research, various elementary properties of modules over rings are generalized to properties of hypermodules over Krasner hyperrings and some concrete examples of hypermodules over Krasner hyperrings are given by considering among the collection of all multiplicative interval semigroups joining 0 on the system of real numbers and some hyperoperations. Moreover, we give a definition of projective hypermodule which is parallel to the definition of projective module in module theory and study some related properties.
Author: Sopon Boriboon
Publisher:
ISBN:
Category :
Languages : en
Pages : 118
Get Book Here
Book Description
Author: Thomas Vougiouklis
Publisher: World Scientific
ISBN: 9814569453
Category :
Languages : en
Pages : 236
Get Book Here
Book Description
Topics covered include semihypergroups, hypergroups, hyperrings, hyperfields, hypermatrices, ordered hyperstructures etc., related topics as join spaces, cogroups, polygroups and finally applications on combinatorics, field theory, finite geometry, computer science etc.
Author: Bijan Davvaz
Publisher: World Scientific Publishing Company
ISBN: 9789811285400
Category : Mathematics
Languages : en
Pages : 0
Get Book Here
Book Description
The theory of algebraic hyperstructures, in particular the theory of Krasner hyperrings, has seen a spectacular development in the last 20 years, which is why a book dedicated to the study of these is so vital. Krasner hyperrings are a generalization of hyperfields, introduced by Krasner in order to study complete valued fields. A Krasner hyperring (R, +, .) is an algebraic structure, where (R, +) is a canonical hypergroup, (R, .) is a semigroup having zero as a bilaterally absorbing element and the multiplication is distributive with respect to the hyperoperation +.Krasner Hyperring Theory presents an elaborate study on hyperstructures, particularly Krasner hyperrings, across 10 chapters with extensive examples. It contains the results of the authors, but also of other researchers in the field, focusing especially on recent research. This book is especially addressed to doctoral students or researchers in the field, as well as to all those interested in this interesting part of algebra, with applications in other fields.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 542
Get Book Here
Book Description
Author: Bijan Davvaz
Publisher: World Scientific
ISBN: 9811249407
Category : Mathematics
Languages : en
Pages : 300
Get Book Here
Book Description
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.
Author: Piergiulio Corsini
Publisher:
ISBN:
Category : Hypergroups
Languages : en
Pages : 224
Get Book Here
Book Description
Author: Joan Cabestany
Publisher: Springer
ISBN: 3642214983
Category : Computers
Languages : en
Pages : 725
Get Book Here
Book Description
This two-volume set LNCS 6691 and 6692 constitutes the refereed proceedings of the 11th International Work-Conference on Artificial Neural Networks, IWANN 2011, held in Torremolinos-Málaga, Spain, in June 2011. The 154 revised papers were carefully reviewed and selected from 202 submissions for presentation in two volumes. The second volume includes 76 papers organized in topical sections on video and image processing; hybrid artificial neural networks: models, algorithms and data; advances in machine learning for bioinformatics and computational biomedicine; biometric systems for human-machine interaction; data mining in biomedicine; bio-inspired combinatorial optimization; applying evolutionary computation and nature-inspired algorithms to formal methods; recent advances on fuzzy logic and soft computing applications; new advances in theory and applications of ICA-based algorithms; biological and bio-inspired dynamical systems; and interactive and cognitive environments. The last section contains 9 papers from the International Workshop on Intelligent Systems for Context-Based Information Fusion, ISCIF 2011, held at IWANN 2011.
Author: Bijan Davvaz
Publisher: Springer Nature
ISBN: 9811661081
Category : Mathematics
Languages : en
Pages : 285
Get Book Here
Book Description
This textbook provides a readable account of the examples and fundamental results of groups from a theoretical and geometrical point of view. This is the second book of the set of two books on groups theory. Topics on linear transformation and linear groups, group actions on sets, Sylow’s theorem, simple groups, products of groups, normal series, free groups, platonic solids, Frieze and wallpaper symmetry groups and characters of groups have been discussed in depth. Covering all major topics, this book is targeted to advanced undergraduate students of mathematics with no prerequisite knowledge of the discussed topics. Each section ends with a set of worked-out problems and supplementary exercises to challenge the knowledge and ability of the reader.
Author: Bijan Davvaz
Publisher: Springer
ISBN: 3319147625
Category : Technology & Engineering
Languages : en
Pages : 250
Get Book Here
Book Description
This book is intended as an introduction to fuzzy algebraic hyperstructures. As the first in its genre, it includes a number of topics, most of which reflect the authors’ past research and thus provides a starting point for future research directions. The book is organized in five chapters. The first chapter introduces readers to the basic notions of algebraic structures and hyperstructures. The second covers fuzzy sets, fuzzy groups and fuzzy polygroups. The following two chapters are concerned with the theory of fuzzy Hv-structures: while the third chapter presents the concept of fuzzy Hv-subgroup of Hv-groups, the fourth covers the theory of fuzzy Hv-ideals of Hv-rings. The final chapter discusses several connections between hypergroups and fuzzy sets, and includes a study on the association between hypergroupoids and fuzzy sets endowed with two membership functions. In addition to providing a reference guide to researchers, the book is also intended as textbook for undergraduate and graduate students.
