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: 1.61 MB
Reproduction Date: 8/2/2013

Title: Non Associative Algebraic Structures Using Finite Complex Numbers  
Author: Smarandache, Florentin
Language: English
Subject: Non Fiction, Education, Algebra
Collections: Authors Community, Mathematics
Publication Date:
Publisher: World Public Library
Member Page: Florentin Smarandache


APA MLA Chicago

Smarandache, B. F., & Vasantha Kandasamy, W. B. (2013). Non Associative Algebraic Structures Using Finite Complex Numbers. Retrieved from

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.

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.


Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg 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.