Krasner Hyperring Theory

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Krasner Hyperring Theory

Author : Bijan Davvaz
Publisher : World Scientific
ISBN 13 : 981128542X
Total Pages : 308 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Krasner Hyperring Theory by : Bijan Davvaz

Download or read book Krasner Hyperring Theory written by Bijan Davvaz and published by World Scientific. This book was released on 2024-02-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Hypergroup Theory

Author : Bijan Davvaz
Publisher : World Scientific
ISBN 13 : 9811249407
Total Pages : 300 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Hypergroup Theory by : Bijan Davvaz

Download or read book Hypergroup Theory written by Bijan Davvaz and published by World Scientific. This book was released on 2021-12-28 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebra, Graph Theory and their Applications

Author : T.T Chelvam
Publisher : ALPHA SCIENCE INTERNATIONAL LIMITED
ISBN 13 : 8184873107
Total Pages : 370 pages
Book Rating : 4.1/5 (848 download)

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Book Synopsis Algebra, Graph Theory and their Applications by : T.T Chelvam

Download or read book Algebra, Graph Theory and their Applications written by T.T Chelvam and published by ALPHA SCIENCE INTERNATIONAL LIMITED. This book was released on 2009-12-03 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra and Graph Theory are two fascinating branches of Mathematics. The tools of each have been used in the other to explore and investigate problems in depth. Especially the Cayley graphs constructed out of the group structures have been greatly and extensively used in Parallel computers to provide network to the routing problem. ALGEBRA, GRAPH THEORY AND THEIR APPLICATIONS takes an inclusive view of the two areas and presents a wide range of topics. It includes sixteen referred research articles on algebra and graph theory of which three are expository in nature alongwith articles exhibiting the use of algebraic techniques in the study of graphs. A substantial proportion of the book covers topics that have not yet appeared in book form providing a useful resource to the younger generation of researchers in Discrete Mathematics.

Groups and Symmetry

Author : Bijan Davvaz
Publisher : Springer Nature
ISBN 13 : 9811661081
Total Pages : 285 pages
Book Rating : 4.8/5 (116 download)

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Book Synopsis Groups and Symmetry by : Bijan Davvaz

Download or read book Groups and Symmetry written by Bijan Davvaz and published by Springer Nature. This book was released on 2021-11-17 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Applications of Hyperstructure Theory

Author : P. Corsini
Publisher : Springer Science & Business Media
ISBN 13 : 1475737149
Total Pages : 333 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Applications of Hyperstructure Theory by : P. Corsini

Download or read book Applications of Hyperstructure Theory written by P. Corsini and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents some of the numerous applications of hyperstructures, especially those that were found and studied in the last fifteen years. There are applications to the following subjects: 1) geometry; 2) hypergraphs; 3) binary relations; 4) lattices; 5) fuzzy sets and rough sets; 6) automata; 7) cryptography; 8) median algebras, relation algebras; 9) combinatorics; 10) codes; 11) artificial intelligence; 12) probabilities. Audience: Graduate students and researchers.

Coding Theory

Author : Sudhakar Radhakrishnan
Publisher : BoD – Books on Demand
ISBN 13 : 1839694092
Total Pages : 142 pages
Book Rating : 4.8/5 (396 download)

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Book Synopsis Coding Theory by : Sudhakar Radhakrishnan

Download or read book Coding Theory written by Sudhakar Radhakrishnan and published by BoD – Books on Demand. This book was released on 2022-05-25 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the latest developments, methods, approaches, and applications of coding theory in a wide variety of fields and endeavors. It consists of seven chapters that address such topics as applications of coding theory in networking and cryptography, wireless sensor nodes in wireless body area networks, the construction of linear codes, and more.

Prolegomena of Hypergroup Theory

Author : Piergiulio Corsini
Publisher :
ISBN 13 :
Total Pages : 224 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Prolegomena of Hypergroup Theory by : Piergiulio Corsini

Download or read book Prolegomena of Hypergroup Theory written by Piergiulio Corsini and published by . This book was released on 1994 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Hyperring theory and applications

Author :
Publisher :
ISBN 13 : 9781574850642
Total Pages : pages
Book Rating : 4.8/5 (56 download)

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Book Synopsis Hyperring theory and applications by :

Download or read book Hyperring theory and applications written by and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Casimir Force, Casimir Operators and the Riemann Hypothesis

Author : Gerrit van Dijk
Publisher : Walter de Gruyter
ISBN 13 : 311022612X
Total Pages : 295 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Casimir Force, Casimir Operators and the Riemann Hypothesis by : Gerrit van Dijk

Download or read book Casimir Force, Casimir Operators and the Riemann Hypothesis written by Gerrit van Dijk and published by Walter de Gruyter. This book was released on 2010 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Recent Developments in Algebra and Analysis

Author : Ho-Hon Leung
Publisher : Springer Nature
ISBN 13 : 3031375386
Total Pages : 383 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Recent Developments in Algebra and Analysis by : Ho-Hon Leung

Download or read book Recent Developments in Algebra and Analysis written by Ho-Hon Leung and published by Springer Nature. This book was released on with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt:

NeutroGeometry, NeutroAlgebra, and SuperHyperAlgebra in Today's World

Author : Smarandache, Florentin
Publisher : IGI Global
ISBN 13 : 1668447428
Total Pages : 280 pages
Book Rating : 4.6/5 (684 download)

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Book Synopsis NeutroGeometry, NeutroAlgebra, and SuperHyperAlgebra in Today's World by : Smarandache, Florentin

Download or read book NeutroGeometry, NeutroAlgebra, and SuperHyperAlgebra in Today's World written by Smarandache, Florentin and published by IGI Global. This book was released on 2023-05-15 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: NeutroAlgebra and AntiAlgebra were extended to NeutroGeometry and AntiGeometry in order to catch the Non-Euclidean Geometries. In the real world, the spaces and the elements that populate them and the rules that apply to them are not perfect, uniform, homogeneous, or complete. They are fragmentary and disparate, with unclear and conflicting information, and they do not apply in the same degree to each element. Therefore, these partial, hybrid, and mixed structures are necessary. NeutroGeometry, NeutroAlgebra, and SuperHyperAlgebra in Today's World presents applications of many NeutroStructures in our real world and considers NeutroGeometry and AntiGeometry as new fields of research that resemble everyday life. Covering key topics such as hyperbolic geometry, elliptic geometry, and AntiGeometry, this reference work is ideal for mathematicians, industry professionals, researchers, scholars, academicians, practitioners, instructors, and students.

Symmetry in Classical and Fuzzy Algebraic Hypercompositional Structures

Author : Irina Cristea
Publisher : MDPI
ISBN 13 : 3039287087
Total Pages : 208 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis Symmetry in Classical and Fuzzy Algebraic Hypercompositional Structures by : Irina Cristea

Download or read book Symmetry in Classical and Fuzzy Algebraic Hypercompositional Structures written by Irina Cristea and published by MDPI. This book was released on 2020-05-29 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of 12 innovative research papers in the field of hypercompositional algebra, 7 of them being more theoretically oriented, with the other 5 presenting strong applicative aspects in engineering, control theory, artificial intelligence, and graph theory. Hypercompositional algebra is now a well-established branch of abstract algebra dealing with structures endowed with multi-valued operations, also called hyperoperations, having a set as the result of the interrelation between two elements of the support set. The theoretical papers in this book are principally related to three main topics: (semi)hypergroups, hyperfields, and BCK-algebra. Heidari and Cristea present a natural generalization of breakable semigroups, defining the breakable semihypergroups where every non-empty subset is a subsemihypergroup. Using the fundamental relation β on a hypergroup, some new properties of the β-classes are obtained by De Salvo et al., who introduced and investigated the notion of height of a β-class. Based on the properties of a cyclic hypergroup of particular matrices, Krehlik and Vyroubalova describe the symmetry of lower and upper approximations in certain rough sets connected with this hypergroup. These results suggest an application to the study of detection sensors. In the framework of hyperrings and hyperfields theory, a new line of research has been developed regarding hyperhomographies on Krasner hyperfields, with interesting applications in cryptography (Vahedi et al.) and new fuzzy weak hyperideals were defined in Hv-rings by using the concept of fuzzy multiset (Al Tahan et al.), for which some algebraic properties were obtained. Two articles are dedicated to the study of BCK-algebras. Bordbar et al. present the properties of the relative annihilator in lower BCK-semilattices, whereas several types of intuitionistic fuzzy soft ideals in hyper BCK-algebras were defined and studied by Xin et al. Increasing numbers of researchers are interested in the applicative aspects of algebraic hypercompositional structures. For example, new properties related with symmetric relations are emphasized by Chvalina and Smetana for the structures and hyperstructures of artificial neurons. Novak et al. present a mathematical model based on elements of algebraic hyperstructure theory, used in the context of underwater wireless sensor networks. A construction of granular structures using m-polar fuzzy hypergraphs and level hypergraphs is illustrated in Luqman et al. using examples from a real-life problem. In the last paper in this book, Akram et al. discuss some properties related to edge regularity for q-rung picture fuzzy graphs.

Hyperstructures and Their Representations

Author : Thomas Vougiouklis
Publisher :
ISBN 13 :
Total Pages : 206 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Hyperstructures and Their Representations by : Thomas Vougiouklis

Download or read book Hyperstructures and Their Representations written by Thomas Vougiouklis and published by . This book was released on 1994 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advances in the Theory of Numbers

Author : Ayşe Alaca
Publisher : Springer
ISBN 13 : 1493932012
Total Pages : 235 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Advances in the Theory of Numbers by : Ayşe Alaca

Download or read book Advances in the Theory of Numbers written by Ayşe Alaca and published by Springer. This book was released on 2015-10-28 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of numbers continues to occupy a central place in modern mathematics because of both its long history over many centuries as well as its many diverse applications to other fields such as discrete mathematics, cryptography, and coding theory. The proof by Andrew Wiles (with Richard Taylor) of Fermat’s last theorem published in 1995 illustrates the high level of difficulty of problems encountered in number-theoretic research as well as the usefulness of the new ideas arising from its proof. The thirteenth conference of the Canadian Number Theory Association was held at Carleton University, Ottawa, Ontario, Canada from June 16 to 20, 2014. Ninety-nine talks were presented at the conference on the theme of advances in the theory of numbers. Topics of the talks reflected the diversity of current trends and activities in modern number theory. These topics included modular forms, hypergeometric functions, elliptic curves, distribution of prime numbers, diophantine equations, L-functions, Diophantine approximation, and many more. This volume contains some of the papers presented at the conference. All papers were refereed. The high quality of the articles and their contribution to current research directions make this volume a must for any mathematics library and is particularly relevant to researchers and graduate students with an interest in number theory. The editors hope that this volume will serve as both a resource and an inspiration to future generations of researchers in the theory of numbers.

Fuzzy Algebraic Hyperstructures

Author : Bijan Davvaz
Publisher : Springer
ISBN 13 : 3319147625
Total Pages : 250 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Fuzzy Algebraic Hyperstructures by : Bijan Davvaz

Download or read book Fuzzy Algebraic Hyperstructures written by Bijan Davvaz and published by Springer. This book was released on 2015-01-23 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

International Journal of Neutrosophic Science (IJNS) Volume 5, 2020

Author : Broumi Said
Publisher : Infinite Study
ISBN 13 :
Total Pages : 106 pages
Book Rating : 4./5 ( download)

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Book Synopsis International Journal of Neutrosophic Science (IJNS) Volume 5, 2020 by : Broumi Said

Download or read book International Journal of Neutrosophic Science (IJNS) Volume 5, 2020 written by Broumi Said and published by Infinite Study. This book was released on with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Journal of Neutrosophic Science (IJNS) is a peer-review journal publishing high quality experimental and theoretical research in all areas of Neutrosophic and its Applications. IJNS is published quarterly. IJNS is devoted to the publication of peer-reviewed original research papers lying in the domain of neutrosophic sets and systems. Papers submitted for possible publication may concern with foundations, neutrosophic logic and mathematical structures in the neutrosophic setting. Besides providing emphasis on topics like artificial intelligence, pattern recognition, image processing, robotics, decision making, data analysis, data mining, applications of neutrosophic mathematical theories contributing to economics, finance, management, industries, electronics, and communications are promoted.

International Journal of Neutrosophic Science (IJNS) Volume 8, 2020

Author : Broumi Said
Publisher : Infinite Study
ISBN 13 :
Total Pages : 126 pages
Book Rating : 4./5 ( download)

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Book Synopsis International Journal of Neutrosophic Science (IJNS) Volume 8, 2020 by : Broumi Said

Download or read book International Journal of Neutrosophic Science (IJNS) Volume 8, 2020 written by Broumi Said and published by Infinite Study. This book was released on with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Journal of Neutrosophic Science (IJNS) is a peer-review journal publishing high quality experimental and theoretical research in all areas of Neutrosophic and its Applications. IJNS is published quarterly. IJNS is devoted to the publication of peer-reviewed original research papers lying in the domain of neutrosophic sets and systems. Papers submitted for possible publication may concern with foundations, neutrosophic logic and mathematical structures in the neutrosophic setting. Besides providing emphasis on topics like artificial intelligence, pattern recognition, image processing, robotics, decision making, data analysis, data mining, applications of neutrosophic mathematical theories contributing to economics, finance, management, industries, electronics, and communications are promoted.