Overview

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.

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9780367380045

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Reviews

The book is quite self-contained in that the introduction describes the basic concepts covered in the rest of the book, including some notions on fuzzy sets and fuzzy algebraic groups. ... The vast majority of the results, even preliminary ones, are accompanied by proofs, making the book quite interesting for readers who want to get acquainted with the theory of near rings. -Computing Reviews, October 2013 The authors present the theory of near rings, and conclude with two chapters on the application to fuzzy ideals and graph theoretical investigations in near rings. ... The book is quite self-contained, in that the introduction describes the basic concepts covered in the rest of the book, including some notions on fuzzy sets and fuzzy algebraic groups. The content is organized in a standard way, with numbering of definitions, lemmas, examples, and notes. Most of the definitions and results are accompanied by references to the literature, mainly to previous results produced by the authors or to other books written by some of the authors. The vast majority of the results, even preliminary ones, are accompanied by proofs, making the book quite interesting for readers who want to get acquainted with the theory of near rings. Since most of the book is really about near rings, the target audience includes readers that are interested in near rings and in ring properties that transfer to near rings and their connection to geometry. -Marcelo Finger, Computing Reviews, October 2013

The book is quite self-contained in that the introduction describes the basic concepts covered in the rest of the book, including some notions on fuzzy sets and fuzzy algebraic groups. ... The vast majority of the results, even preliminary ones, are accompanied by proofs, making the book quite interesting for readers who want to get acquainted with the theory of near rings. --Computing Reviews, October 2013 The authors present the theory of near rings, and conclude with two chapters on the application to fuzzy ideals and graph theoretical investigations in near rings. ... The book is quite self-contained, in that the introduction describes the basic concepts covered in the rest of the book, including some notions on fuzzy sets and fuzzy algebraic groups. The content is organized in a standard way, with numbering of definitions, lemmas, examples, and notes. Most of the definitions and results are accompanied by references to the literature, mainly to previous results produced by the authors or to other books written by some of the authors. The vast majority of the results, even preliminary ones, are accompanied by proofs, making the book quite interesting for readers who want to get acquainted with the theory of near rings. Since most of the book is really about near rings, the target audience includes readers that are interested in near rings and in ring properties that transfer to near rings and their connection to geometry. --Marcelo Finger, Computing Reviews, October 2013

""The book is quite self-contained in that the introduction describes the basic concepts covered in the rest of the book, including some notions on fuzzy sets and fuzzy algebraic groups. … The vast majority of the results, even preliminary ones, are accompanied by proofs, making the book quite interesting for readers who want to get acquainted with the theory of near rings."" —Computing Reviews, October 2013 ""The authors present the theory of near rings, and conclude with two chapters on the application to fuzzy ideals and graph theoretical investigations in near rings. ... The book is quite self-contained, in that the introduction describes the basic concepts covered in the rest of the book, including some notions on fuzzy sets and fuzzy algebraic groups. The content is organized in a standard way, with numbering of definitions, lemmas, examples, and notes. Most of the definitions and results are accompanied by references to the literature, mainly to previous results produced by the authors or to other books written by some of the authors. The vast majority of the results, even preliminary ones, are accompanied by proofs, making the book quite interesting for readers who want to get acquainted with the theory of near rings. Since most of the book is really about near rings, the target audience includes readers that are interested in near rings and in ring properties that transfer to near rings and their connection to geometry."" —Marcelo Finger, Computing Reviews, October 2013

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Satyanarayana, Bhavanari; Prasad, Kuncham Syam

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