Near Rings, Fuzzy Ideals, and Graph Theory: 1st Edition (Paperback) book cover

Near Rings, Fuzzy Ideals, and Graph Theory

1st Edition

By Bhavanari Satyanarayana, Kuncham Syam Prasad

Chapman and Hall/CRC

480 pages

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Description

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.

Table of Contents

Preliminaries. Fundamentals of Near Rings. More Concepts on Near Rings. Prime and Semiprime Ideals. Dimension and Decomposition Theory. Matrix Near Rings. Gamma Near Rings. Fuzzy Aspects in Near Rings and Gamma Near Rings. Fundamental Concepts of Graph Theory. References. Index.

About the Authors

Satyanarayana, Bhavanari; Prasad, Kuncham Syam

Subject Categories

BISAC Subject Codes/Headings:
COM046000
COMPUTERS / Operating Systems / General
MAT000000
MATHEMATICS / General
MAT002000
MATHEMATICS / Algebra / General
MAT036000
MATHEMATICS / Combinatorics