Near Rings, Fuzzy Ideals, and Graph Theory (Hardcover)
暫譯: 近環、模糊理想與圖論 (精裝版)

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之間的關係,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。

在介紹所有必要的代數系統基礎後,本書呈現了近環理論的基本要素、相關範例、符號及簡單定理。接著,書中描述了近環中的質理想概念,對群的維度理論採取嚴謹的方式,提供了一些矩陣近環的詳細證明,並討論了伽瑪近環,這是一種伽瑪環和近環的概括。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、質圖以及與近環中的理想相關的圖。

近環理論在數位計算、序列力學、自動機理論、圖論和組合學等多個領域有著廣泛的應用。本書適合研究人員和研究生,幫助讀者理解近環理論及其與模糊理想和圖論的聯繫。