World Library  


Add to Book Shelf
Flag as Inappropriate
Email this Book

Non Associative Algebraic Structures Using Finite Complex Numbers

By Smarandache, Florentin

Click here to view

Book Id: WPLBN0002828486
Format Type: PDF (eBook)
File Size: 1.53 mb
Reproduction Date: 8/2/2013

Title: Non Associative Algebraic Structures Using Finite Complex Numbers  
Author: Smarandache, Florentin
Volume:
Language: English
Subject: Non Fiction, Education, Algebra
Collections: Mathematics, Algebra, Mathematical Analysis, Math, Authors Community, Arithmetic, Education, Most Popular Books in China, Literature, Science
Historic
Publication Date:
2013
Publisher: World Public Library
Member Page: Florentin Smarandache

Citation

APA MLA Chicago

Smarandache, F., & Vasantha Kandasamy, W. B. (2013). Non Associative Algebraic Structures Using Finite Complex Numbers. Retrieved from http://www.worldebooklibrary.com/


Description
This book has six chapters. The first one is introductory in nature. Second chapter introduces complex modulo integer groupoids and complex modulo integer loops using C(Zn). This chapter gives 77 examples and forty theorems. Chapter three introduces the notion of nonassociative complex rings both finite and infinite using complex groupoids and complex loops. This chapter gives over 120 examples and thirty theorems. Forth chapter introduces nonassociative structures using complex modulo integer groupoids and quasi loops. This new notion is well illustrated by 140 examples. These can find applications only in due course of time, when these new concepts become familiar. The final chapter suggests over 300 problems some of which are research problems.

Summary
Authors in this book for the first time have constructed nonassociative structures like groupoids, quasi loops, non associative semirings and rings using finite complex modulo integers. The Smarandache analogue is also carried out. We see the nonassociative complex modulo integers groupoids satisfy several special identities like Moufang identity, Bol identity, right alternative and left alternative identities. P-complex modulo integer groupoids and idempotent complex modulo integer groupoids are introduced and characterized.

Table of Contents
THEOREM 2.1: Let G = {C(Zn), *, (t, u); t, u ∈ Zn} be a complex modulo integer groupoid. If H ⊆ G is such that H is a Smarandache modulo integer subgroupoid, then G is a Smarandache complex modulo integer groupoid. But every subgroupoid of G need not be a Smarandache complex modulo interger subgroupoid even if G is a Smarandache groupoid. Proof is direct and hence is left as an exercise to the reader. Example 2.28: Consider G = {C(Z8), *, (2, 4)}, a complex modulo integer groupoid.

 

Click To View

Additional Books


  • Rhodesialeaks : Financial History of Eco... Volume 1 (by )
  • Ai'Ai (by )
  • Survival Scenarios and Suggestions Volume 1 (by )
  • Fantastic Trillion : Saga (by )
  • Submission by PVCHR regarding India for ... (by )
  • Transformation Through Bodywork : Using ... (by )
  • Trei Povestiri (by )
  • Eco Escuela : Ideas para habitar el plan... (by )
  • A Guide To the Hidden Wisdom of Kabbalah (by )
  • A Guide To the Hidden Wisdom of Kabbalah (by )
  • Camisea: Emerging Lessons in Development... (by )
  • Science History of the Universe (by )
Scroll Left
Scroll Right

 



Copyright © World Library Foundation. All rights reserved. eBooks from World eBook 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.