Near rings, fuzzy ideals, and graph theory
- Satyanarayana, Bhavanari.
- Boca Raton : CRC Press, Taylor & Francis Group, 
- Copyright notice
- Physical description
- xi, 468 pages : illustrations ; 24 cm
QA251.5 .S28 2013
- Unknown QA251.5 .S28 2013
- Prasad, Kuncham Syam.
- Includes bibliographical references (pages 453-458) and index.
- Preliminaries Set Theory Group Theory Ring Theory Vector Spaces Module Theory Graphs Introduction to Fuzzy Sets Some Fuzzy Algebraic Systems Fundamentals of Near Rings Definitions and Examples Substructures of Near Rings and Quotient Near Rings Homomorphism and Isomorphism Introduction to Matrix Near Rings More Concepts on Near Rings N-Groups Homomorphisms in N-Groups Chain Conditions on Ideals Direct Systems in N-Groups Some Results on Mn(N)-Group Nn Prime and Semiprime Ideals Fundamental Definitions and Results Prime Radicals in Near Rings Insertion of Factors Property Ideals in Near Rings and N-Groups Finite Spanning Dimension in N-Groups Dimension and Decomposition Theory Finite Goldie Dimension Linearly Independent Elements in N-Groups Primary Decomposition in Near Rings Tertiary Decomposition in N-Groups Matrix Near Rings Preliminary Results Prime Ideals in Matrix Near Rings Finite Goldie Dimension in Mn(N)-Group Nn Gamma Near Rings Definitions and Examples Ideals of Gamma Near Rings Prime Ideals and Nilpotent Ideals in Gamma Near Rings Modules over Gamma Near Rings Fuzzy Aspects in Near Rings and Gamma Near Rings Fuzzy Ideals and Prime Ideals in Gamma Near Rings Fuzzy Cosets of Gamma Near Rings Fuzzy Ideals of MGAMMA-Groups Homomorphisms and Fuzzy Cosets of MGAMMA-Groups Fuzzy Dimension in N-Groups Fundamental Concepts of Graph Theory Introduction Directed Hypercubes Vector Spaces of a Graph Prime Graph of a Ring Homomorphism of Graphs Graph of a Near Ring with Respect to an Ideal References Index.
- (source: Nielsen Book Data)
- Publisher's Summary
- 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.
(source: Nielsen Book Data)
- Publication date
- Copyright date
- Bhavanari Satyanarayana, Kuncham Syam Prasad.