World Library  


Add to Book Shelf
Flag as Inappropriate
Email this Book

Neutrosophic Rings

By Smarandache, Florentin

Click here to view

Book Id: WPLBN0002828478
Format Type: PDF (eBook)
File Size: 593.86 kb
Reproduction Date: 8/2/2013

Title: Neutrosophic Rings  
Author: Smarandache, Florentin
Volume:
Language: English
Subject: Non Fiction, Education, Neutrosophic Logic
Collections: Mathematics, Logic, Authors Community, Algebra, Math, Education, Most Popular Books in China, Literature
Historic
Publication Date:
2013
Publisher: World Public Library
Member Page: Florentin Smarandache

Citation

APA MLA Chicago

Smarandache, F., & Vasantha Kandasamy, W. B. (2013). Neutrosophic Rings. Retrieved from http://kindle.worldlibrary.net/


Description
This book has four chapters. Chapter one is introductory in nature, for it recalls some basic definitions essential to make the book a self-contained one. Chapter two, introduces for the first time the new notion of neutrosophic rings and some special neutrosophic rings like neutrosophic ring of matrix and neutrosophic polynomial rings. Chapter three gives some new classes of neutrosophic rings like group neutrosophic rings, neutrosophic group neutrosophic rings, semigroup neutrosophic rings, S-semigroup neutrosophic rings which can be realized as a type of extension of group rings or generalization of group rings. Study of these structures will throw light on the research on the algebraic structure of group rings. Chapter four is entirely devoted to the problems on this new topic, which is an added attraction to researchers. A salient feature of this book is that it gives 246 problems in Chapter four. Some of the problems are direct and simple, some little difficult and some can be taken up as a research problem.

Summary
In this book we define the new notion of neutrosophic rings.

Excerpt
Now we proceed onto define the notion of neutrosophic subgroup of a neutrosophic group. DEFINITION 1.1.2: Let N(G) = 〈G ∪ I〉 be a neutrosophic group generated by G and I. A proper subset P(G) is said to be a neutrosophic subgroup if P(G) is a neutrosophic group i.e. P(G) must contain a (sub) group. Example 1.1.3: Let N(Z2) = 〈Z2 ∪ I〉 be a neutrosophic group under addition. N(Z2) = {0, 1, I, 1 + I}. Now we see {0, I} is a group under + in fact a neutrosophic group {0, 1 + I} is a group under ‘+’ but we call {0, I} or {0, 1 + I} only as pseudo neutrosophic groups for they do not have a proper subset which is a group. So {0, I} and {0, 1 + I} will be only called as pseudo neutrosophic groups (subgroups). We can thus define a pseudo neutrosophic group as a neutrosophic group, which does not contain a proper subset which is a group. Pseudo neutrosophic subgroups can be found as a substructure of neutrosophic groups. Thus a pseudo neutrosophic group though has a group structure is not a neutrosophic group and a neutrosophic group cannot be a pseudo neutrosophic group. Both the concepts are different. Now we see a neutrosophic group can have substructures which are pseudo neutrosophic groups which is evident from the following example.

Table of Contents
Preface 5 Chapter One INTRODUCTION 1.1 Neutrosophic Groups and their Properties 7 1.2 Neutrosophic Semigroups 20 1.3 Neutrosophic Fields 27 Chapter Two NEUTROSOPHIC RINGS AND THEIR PROPERTIES 2.1 Neutrosophic Rings and their Substructures 29 2.2 Special Type of Neutrosophic Rings 41 Chapter Three NEUTROSOPHIC GROUP RINGS AND THEIR GENERALIZATIONS 3.1 Neutrosophic Group Rings 59 3.2 Some special properties of Neutrosophic Group Rings 73 3.3 Neutrosophic Semigroup Rings and their Generalizations 85 Chapter Four SUGGESTED PROBLEMS 107 REFERENCES 135 INDEX 149 ABOUT THE AUTHORS 154

 

Click To View

Additional Books


  • Ruling Chiefs of Hawaii (by )
  • Ko Pele Hiki 'Ana Mai I Hawai'I (by )
  • A Tale of Two Cities (by )
  • Glorious Ukrainian Bride Wants YOU!: Sto... (by )
  • Hawaii Place Names (by )
  • Aia He Kaheka (by )
  • Learning the Code 
  • The Loudest Voice in the World (by )
  • Easy : Dashuria nuk është gjithmonë e le... (by )
  • Belief of the Reborn (by )
  • A Guide To the Hidden Wisdom of Kabbalah (by )
  • الآداب والأخلاق : نشرة شهرية تعني بشؤون ... (by )
Scroll Left
Scroll Right

 



Copyright © World Library Foundation. All rights reserved. eBooks from World eBook Library on the Kindle are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.