The Graphs Associated With Rings

Author : David F. Anderson,T. Asir,Ayman Badawi,T. Tamizh Chelvam
Publisher : Springer Nature
Page : 548 pages
File Size : 54,7 Mb
Release : 2021-10-31
Category : Mathematics
ISBN : 9783030884109

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Graphs from Rings by David F. Anderson,T. Asir,Ayman Badawi,T. Tamizh Chelvam Pdf

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.

Author : Sumi T,Anto A M
Publisher : Eliva Press
Page : 0 pages
File Size : 48,5 Mb
Release : 2023-06-08
Category : Electronic
ISBN : 9994988557

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The Graphs Associated with Rings by Sumi T,Anto A M Pdf

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.

Author : David F. Anderson,T. Asir,Ayman Badawi,T. Tamizh Chelvam
Publisher : Unknown
Page : 0 pages
File Size : 51,5 Mb
Release : 2021
Category : Electronic
ISBN : 3030884112

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Graphs from Rings by David F. Anderson,T. Asir,Ayman Badawi,T. Tamizh Chelvam Pdf

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.

Author : Bhavanari Satyanarayana,Kuncham Syam Prasad
Publisher : CRC Press
Page : 482 pages
File Size : 54,8 Mb
Release : 2013-05-21
Category : Computers
ISBN : 9781439873106

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Near Rings, Fuzzy Ideals, and Graph Theory by Bhavanari Satyanarayana,Kuncham Syam Prasad Pdf

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.

Author : P. Balasubramaniam,Kuru Ratnavelu,Grienggrai Rajchakit,G. Nagamani
Publisher : Springer Nature
Page : 349 pages
File Size : 42,7 Mb
Release : 2022-01-13
Category : Mathematics
ISBN : 9789811660184

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Mathematical Modelling and Computational Intelligence Techniques by P. Balasubramaniam,Kuru Ratnavelu,Grienggrai Rajchakit,G. Nagamani Pdf

This book collects papers presented at the International Conference on Mathematical Modelling and Computational Intelligence Techniques (ICMMCIT) 2021, held at the Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram, Tamil Nadu, India, from 10–12 February 2021. Significant contributions from renowned researchers from fields of applied analysis, mathematical modelling and computing techniques have been received for this conference. Chapters emphasize on the research of computational nature focusing on new algorithms, their analysis and numerical results, as well as applications in physical, biological, social, and behavioural sciences. The accepted papers are organized in topical sections as mathematical modelling, image processing, control theory, graphs and networks, and inventory control.

Author : Marco Fontana,Salah-Eddine Kabbaj,Bruce Olberding,Irena Swanson
Publisher : Springer Science & Business Media
Page : 491 pages
File Size : 45,6 Mb
Release : 2010-09-29
Category : Mathematics
ISBN : 9781441969903

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Commutative Algebra by Marco Fontana,Salah-Eddine Kabbaj,Bruce Olberding,Irena Swanson Pdf

Commutative algebra is a rapidly growing subject that is developing in many different directions. This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutative algebra. This volume contains a collection of invited survey articles by some of the leading experts in the field. The authors of these chapters have been carefully selected for their important contributions to an area of commutative-algebraic research. Some topics presented in the volume include: generalizations of cyclic modules, zero divisor graphs, class semigroups, forcing algebras, syzygy bundles, tight closure, Gorenstein dimensions, tensor products of algebras over fields, as well as many others. This book is intended for researchers and graduate students interested in studying the many topics related to commutative algebra.

Author : Denes König
Publisher : Springer Science & Business Media
Page : 430 pages
File Size : 49,5 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781468489712

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Theory of Finite and Infinite Graphs by Denes König Pdf

To most graph theorists there are two outstanding landmarks in the history of their subject. One is Euler's solution of the Konigsberg Bridges Problem, dated 1736, and the other is the appearance of Denes Konig's textbook in 1936. "From Konigsberg to Konig's book" sings the poetess, "So runs the graphic tale . . . " 10]. There were earlier books that took note of graph theory. Veb len's Analysis Situs, published in 1931, is about general combinato rial topology. But its first two chapters, on "Linear graphs" and "Two-Dimensional Complexes," are almost exclusively concerned with the territory still explored by graph theorists. Rouse Ball's Mathematical Recreations and Essays told, usually without proofs, of the major graph-theoretical advances ofthe nineteenth century, of the Five Colour Theorem, of Petersen's Theorem on I-factors, and of Cayley's enumerations of trees. It was Rouse Ball's book that kindled my own graph-theoretical enthusiasm. The graph-theoretical papers of Hassler Whitney, published in 1931-1933, would have made an excellent textbook in English had they been collected and published as such. But the honour of presenting Graph Theory to the mathe matical world as a subject in its own right, with its own textbook, belongs to Denes Konig. Low was the prestige of Graph Theory in the Dirty Thirties. It is still remembered, with resentment now shading into amuse ment, how one mathematician scorned it as "The slums of Topol ogy.""

Author : Manfred Droste,László Fuchs,Brendan Goldsmith,Lutz Strüngmann
Publisher : Springer
Page : 475 pages
File Size : 53,7 Mb
Release : 2017-06-02
Category : Mathematics
ISBN : 9783319517186

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Groups, Modules, and Model Theory - Surveys and Recent Developments by Manfred Droste,László Fuchs,Brendan Goldsmith,Lutz Strüngmann Pdf

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.

Author : Michio Suzuki
Publisher : Unknown
Page : 128 pages
File Size : 42,6 Mb
Release : 1986
Category : Group theory
ISBN : OCLC:471908359

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Group Theory by Michio Suzuki Pdf

Author : Mark R.T. Dale
Publisher : Cambridge University Press
Page : 355 pages
File Size : 43,9 Mb
Release : 2017-11-09
Category : Mathematics
ISBN : 9781107089310

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Applying Graph Theory in Ecological Research by Mark R.T. Dale Pdf

This book clearly describes the many applications of graph theory to ecological questions, providing instruction and encouragement to researchers.

Author : ELHAM MEHDI-NEZHAD,AMIR M. RAHIMI
Publisher : Infinite Study
Page : 12 pages
File Size : 41,6 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 8210379456XXX

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THE SMARANDACHE VERTICES OF THE COMAXIMAL GRAPH OF A COMMUTATIVE RING by ELHAM MEHDI-NEZHAD,AMIR M. RAHIMI Pdf

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).

Author : Gary Chartrand,Ortrud R. Oellermann
Publisher : McGraw-Hill Companies
Page : 424 pages
File Size : 49,7 Mb
Release : 1993
Category : Mathematics
ISBN : UCSC:32106010895685

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Applied and Algorithmic Graph Theory by Gary Chartrand,Ortrud R. Oellermann Pdf

Designed as a bridge to cross the gap between mathematics and computer science, and planned as the mathematics base for computer science students, this maths text is designed to help the student develop an understanding of the concept of an efficient algorithm.

Author : T.Y. Lam
Publisher : Springer Science & Business Media
Page : 410 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468404067

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A First Course in Noncommutative Rings by T.Y. Lam Pdf

One of my favorite graduate courses at Berkeley is Math 251, a one-semester course in ring theory offered to second-year level graduate students. I taught this course in the Fall of 1983, and more recently in the Spring of 1990, both times focusing on the theory of noncommutative rings. This book is an outgrowth of my lectures in these two courses, and is intended for use by instructors and graduate students in a similar one-semester course in basic ring theory. Ring theory is a subject of central importance in algebra. Historically, some of the major discoveries in ring theory have helped shape the course of development of modern abstract algebra. Today, ring theory is a fer tile meeting ground for group theory (group rings), representation theory (modules), functional analysis (operator algebras), Lie theory (enveloping algebras), algebraic geometry (finitely generated algebras, differential op erators, invariant theory), arithmetic (orders, Brauer groups), universal algebra (varieties of rings), and homological algebra (cohomology of rings, projective modules, Grothendieck and higher K-groups). In view of these basic connections between ring theory and other branches of mathemat ics, it is perhaps no exaggeration to say that a course in ring theory is an indispensable part of the education for any fledgling algebraist. The purpose of my lectures was to give a general introduction to the theory of rings, building on what the students have learned from a stan dard first-year graduate course in abstract algebra.

Author : Jeffrey Patrick Angel
Publisher : Unknown
Page : 184 pages
File Size : 45,6 Mb
Release : 1993
Category : Electronic
ISBN : UCSD:31822017741117

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Finite Upper Half Planes Over Finite Rings and Their Associated Graphs by Jeffrey Patrick Angel Pdf

Author : Constantin Nastasescu,Freddy van Oystaeyen
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 47,8 Mb
Release : 2004-02-19
Category : Mathematics
ISBN : 3540207465

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Methods of Graded Rings by Constantin Nastasescu,Freddy van Oystaeyen Pdf

The Category of Graded Rings.- The Category of Graded Modules.- Modules over Stronly Graded Rings.- Graded Clifford Theory.- Internal Homogenization.- External Homogenization.- Smash Products.- Localization of Graded Rings.- Application to Gradability.- Appendix A:Some Category Theory.- Appendix B: Dimensions in an abelian Category.- Bibliography.- Index.-