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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