World Library  


Add to Book Shelf
Flag as Inappropriate
Email this Book

Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures

By Smarandache, Florentin

Click here to view

Book Id: WPLBN0002828472
Format Type: PDF (eBook)
File Size: 1.05 mb
Reproduction Date: 8/2/2013

Title: Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures  
Author: Smarandache, Florentin
Volume:
Language: English
Subject: Non Fiction, Education, Algebra
Collections: Algebra, Mathematics, Math, Authors Community, Education, Literature
Historic
Publication Date:
2013
Publisher: World Public Library
Member Page: Florentin Smarandache

Description
This book has seven chapters. Chapter one provides several basic notions to make this book self-contained. Chapter two introduces neutrosophic groups and neutrosophic N-groups and gives several examples. The third chapter deals with neutrosophic semigroups and neutrosophic N-semigroups, giving several interesting results. Chapter four introduces neutrosophic loops and neutrosophic N-loops. Chapter five just introduces the concept of neutrosophic groupoids and neutrosophic Ngroupoids. Sixth chapter innovatively gives mixed neutrosophic structures and their duals. The final chapter gives problems for the interested reader to solve. Our main motivation is to attract more researchers towards algebra and its various applications.

Summary
In this book, for the first time we introduce the notion of neutrosophic algebraic structures for groups, loops, semigroups and groupoids and also their neutrosophic N-algebraic structures.

Excerpt
1.1 Groups, N-group and their basic Properties It is a well-known fact that groups are the only algebraic structures with a single binary operation that is mathematically so perfect that an introduction of a richer structure within it is impossible. Now we proceed on to define a group. DEFINITION 1.1.1: A non empty set of elements G is said to form a group if in G there is defined a binary operation, called the product and denoted by '•' such that

Table of Contents
Preface 5 Chapter One INTRODUCTION 1.1 Groups, N-group and their basic Properties 7 1.2 Semigroups and N-semigroups 11 1.3 Loops and N-loops 12 1.4 Groupoids and N-groupoids 25 1.5 Mixed N-algebraic Structures 32 Chapter Two NEUTROSOPHIC GROUPS AND NEUTROSOPHIC N-GROUPS 2.1 Neutrosophic Groups and their Properties 40 2.2 Neutrosophic Bigroups and their Properties 52 2.3 Neutrosophic N-groups and their Properties 68 Chapter Three NEUTROSOPHIC SEMIGROUPS AND THEIR GENERALIZATIONS 3.1 Neutrosophic Semigroups 81 3.2 Neutrosophic Bisemigroups and their Properties 88 3.3 Neutrosophic N-Semigroup 98 Chapter Four NEUTROSOPHIC LOOPS AND THEIR GENERALIZATIONS 4.1 Neutrosophic loops and their Properties 113 4.2 Neutrosophic Biloops 133 4.3 Neutrosophic N-loop 152 Chapter five NEUTROSOPHIC GROUPOIDS AND THEIR GENERALIZATIONS 5.1 Neutrosophic Groupoids 171 5.2 Neutrosophic Bigroupoids and their generalizations 182 Chapter Six MIXED NEUTROSOPHIC STRUCTURES 187 Chapter Seven PROBLEMS 195 REFERENCE 201 INDEX 207 ABOUT THE AUTHORS 219

 

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 Library 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.