The Graphs Associated With Rings
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The Graphs Associated With Rings
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Author : Sumi T
language : en
Publisher: Eliva Press
Release Date : 2023-06-08
The Graphs Associated With Rings written by Sumi T and has been published by Eliva Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-08 with categories.
A ring is an abstract structure with a commutative addition, and a multiplication which may or may not be commutative. This distinction yields two quite different theories: the theory of respectively commutative or non-commutative rings. These notes are mainly concerned about commutative rings. Non-commutative rings have been an object of systematic study only quite recently, during the 20th century. Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points does not matter. Each object in a graph is called a node. The subject of graph theory had its beginnings in recreational math problems (see number game), but it has grown into a significant area of mathematical research, with applications in chemistry, operations research, social sciences, and computer science. The study of algebraic structures using the properties of graphs becomes an exciting research topic in the past twenty years, leading to many fascinating results and questions. There are many papers on assigning a graph to a group or a ring. Also, investigation of algebraic properties of groups or rings using the associated graph becomes an exciting topic. In 1999, the zero-divisor graph of a commutative ring Γ(R) was defined by David F. Anderson and Paul S. Livingston as the undirected graph with vertex set Z(R)∗, in which there is an arc from x to y if and only if xy = 0. Through this book, we illustrate some results about the Graphs associated with Rings.
Graphs From Rings
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Author : David F. Anderson
language : en
Publisher: Springer Nature
Release Date : 2021-10-31
Graphs From Rings written by David F. Anderson and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-31 with Mathematics categories.
This book gives an overview of research on graphs associated with commutative rings. The study of the connections between algebraic structures and certain graphs, especially finite groups and their Cayley graphs, is a classical subject which has attracted a lot of interest. More recently, attention has focused on graphs constructed from commutative rings, a field of study which has generated an extensive amount of research over the last three decades. The aim of this text is to consolidate this large body of work into a single volume, with the intention of encouraging interdisciplinary research between algebraists and graph theorists, using the tools of one subject to solve the problems of the other. The topics covered include the graphical and topological properties of zero-divisor graphs, total graphs and their transformations, and other graphs associated with rings. The book will be of interest to researchers in commutative algebra and graph theory and anyone interested in learning about the connections between these two subjects.
Graphs From Rings
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Author : David F. Anderson
language : en
Publisher:
Release Date : 2021
Graphs From Rings written by David F. Anderson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
This book gives an overview of research on graphs associated with commutative rings. The study of the connections between algebraic structures and certain graphs, especially finite groups and their Cayley graphs, is a classical subject which has attracted a lot of interest. More recently, attention has focused on graphs constructed from commutative rings, a field of study which has generated an extensive amount of research over the last three decades. The aim of this text is to consolidate this large body of work into a single volume, with the intention of encouraging interdisciplinary research between algebraists and graph theorists, using the tools of one subject to solve the problems of the other. The topics covered include the graphical and topological properties of zero-divisor graphs, total graphs and their transformations, and other graphs associated with rings. The book will be of interest to researchers in commutative algebra and graph theory and anyone interested in learning about the connections between these two subjects.
Near Rings Fuzzy Ideals And Graph Theory
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Author : Bhavanari Satyanarayana
language : en
Publisher: CRC Press
Release Date : 2013-05-21
Near Rings Fuzzy Ideals And Graph Theory written by Bhavanari Satyanarayana and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-21 with Computers categories.
Near Rings, Fuzzy Ideals, and Graph Theory explores the relationship between near rings and fuzzy sets and between near rings and graph theory. It covers topics from recent literature along with several characterizations. After introducing all of the necessary fundamentals of algebraic systems, the book presents the essentials of near rings theory, relevant examples, notations, and simple theorems. It then describes the prime ideal concept in near rings, takes a rigorous approach to the dimension theory of N-groups, gives some detailed proofs of matrix near rings, and discusses the gamma near ring, which is a generalization of both gamma rings and near rings. The authors also provide an introduction to fuzzy algebraic systems, particularly the fuzzy ideals of near rings and gamma near rings. The final chapter explains important concepts in graph theory, including directed hypercubes, dimension, prime graphs, and graphs with respect to ideals in near rings. Near ring theory has many applications in areas as diverse as digital computing, sequential mechanics, automata theory, graph theory, and combinatorics. Suitable for researchers and graduate students, this book provides readers with an understanding of near ring theory and its connection to fuzzy ideals and graph theory.
Neutrosophic Invertible Graphs Of Neutrosophic Rings
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Author : T. Chalapathi
language : en
Publisher: Infinite Study
Release Date :
Neutrosophic Invertible Graphs Of Neutrosophic Rings written by T. Chalapathi and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
The investigation of simple undirected graphs associated to finite algebraic structures, namely, rings and fields which are very important in the theory of algebraic graphs. In recent years the interplay between Neutrosophic algebraic structure and graph structure is studied by few researchers.
Graphs As Groups
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Author : W. B. Vasantha Kandasamy
language : en
Publisher: Infinite Study
Release Date : 2009
Graphs As Groups written by W. B. Vasantha Kandasamy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
For the first time, every finite group is represented in the form of a graph in this book. This study is significant because properties of groups can be immediately obtained by looking at the graphs of the groups.
The Smarandache Vertices Of The Comaximal Graph Of A Commutative Ring
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Author : ELHAM MEHDI-NEZHAD
language : en
Publisher: Infinite Study
Release Date :
The Smarandache Vertices Of The Comaximal Graph Of A Commutative Ring written by ELHAM MEHDI-NEZHAD and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
The concept of a Smarandache vertex (or S-vertex for short) in a (simple) graph (Definition 2.5) was first introduced by the second author in order to study the Smarandache zero-divisors of a commutative ring which was introduced by Vasantha Kandasamy in for semigroups and rings (not necessarily commutative).
Groups Modules And Model Theory Surveys And Recent Developments
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Author : Manfred Droste
language : en
Publisher: Springer
Release Date : 2017-06-02
Groups Modules And Model Theory Surveys And Recent Developments written by Manfred Droste and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-02 with Mathematics categories.
This volume focuses on group theory and model theory with a particular emphasis on the interplay of the two areas. The survey papers provide an overview of the developments across group, module, and model theory while the research papers present the most recent study in those same areas. With introductory sections that make the topics easily accessible to students, the papers in this volume will appeal to beginning graduate students and experienced researchers alike. As a whole, this book offers a cross-section view of the areas in group, module, and model theory, covering topics such as DP-minimal groups, Abelian groups, countable 1-transitive trees, and module approximations. The papers in this book are the proceedings of the conference “New Pathways between Group Theory and Model Theory,” which took place February 1-4, 2016, in Mülheim an der Ruhr, Germany, in honor of the editors’ colleague Rüdiger Göbel. This publication is dedicated to Professor Göbel, who passed away in 2014. He was one of the leading experts in Abelian group theory.
The Smarandache Vertices Of The Comaximal Graph Of A Commutative Ring
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Author : ELHAM MEHDI-NEZHAD
language : en
Publisher: Infinite Study
Release Date :
The Smarandache Vertices Of The Comaximal Graph Of A Commutative Ring written by ELHAM MEHDI-NEZHAD and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
The main object of this paper is to study the S-vertices of CG(R) and CG2(R) \ J(R) (or CGJ (R) for short), where CG2(R) is the subgraph of CG(R) which consists of nonunit elements of R and J(R) is the Jacobson radical of R. There is also a discussion on a relationship between the diameter and S-vertices of CGJ (R).
Rings Groups And Algebras
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Author : X. Cao
language : en
Publisher: CRC Press
Release Date : 1996-07-23
Rings Groups And Algebras written by X. Cao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-07-23 with Mathematics categories.
"Integrates and summarizes the most significant developments made by Chinese mathematicians in rings, groups, and algebras since the 1950s. Presents both survey articles and recent research results. Examines important topics in Hopf algebra, representation theory, semigroups, finite groups, homology algebra, module theory, valuation theory, and more."