Near Rings, Fuzzy Ideals, and Graph Theory (Hardcover)

Bhavanari Satyanarayana, Kuncham Syam Prasad

  • 出版商: CRC
  • 出版日期: 2013-05-21
  • 售價: $3,300
  • 貴賓價: 9.5$3,135
  • 語言: 英文
  • 頁數: 480
  • 裝訂: Hardcover
  • ISBN: 1439873100
  • ISBN-13: 9781439873106
  • 立即出貨 (庫存 < 3)

商品描述

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.

商品描述(中文翻譯)

《近環、模糊理想與圖論》探討了近環與模糊集合以及近環與圖論之間的關係。書中涵蓋了近期文獻中的主題以及幾個特徵描述。

在介紹了所有必要的代數系統基礎之後,本書介紹了近環理論的基本概念、相關例子、符號和簡單定理。接著描述了近環中的素理想概念,以嚴謹的方式探討了N-群的維度理論,給出了一些矩陣近環的詳細證明,並討論了伽瑪近環,它是伽瑪環和近環的一般化。作者還介紹了模糊代數系統,特別是近環和伽瑪近環的模糊理想。最後一章解釋了圖論中的重要概念,包括有向超立方體、維度、素圖以及關於近環中理想的圖。

近環理論在數位計算、順序力學、自動機理論、圖論和組合數學等領域有許多應用。本書適合研究人員和研究生閱讀,讓讀者了解近環理論及其與模糊理想和圖論的關聯。