Smarandache Loops by W. B. Vasantha Kandasamy
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About this book :-
This book explores a special type of mathematical structure called a loop. A loop is like a group (a group is a well-known concept in algebra), but it doesn’t require everything to follow the rule of associativity (where the grouping of terms doesn’t matter). In this book, she introduces a new idea called a Smarandache loop.
The book entirely lies in the study, introduction and examination of the Smarandache loops based on a paper about Special Algebraic Structures by Florentin Smarandache. The reader should have a good background in algebra and more specifically a strong foundation in loops and number theory.
It obtains some interesting results about them. The notion of Smarandache semigroups homomorphism is studied as well in this paper. Using the definition of homomorphism of Smarandache semi groups we give the classical theorem of Cayley for Smarandache semigroups. It also analyzes the Smarandache loop homomorphism and poses the problem of finding a Cayley theorem for Smarandache loops. Finally it shows that all Smarandache loops Ln(m) for n > 3, n odd, varying n and appropriate m have isomorphic subgroups.
Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B which is embedded with a stronger structure S. By proper subset one understands a set included in A, different from the empty set, from the unit element if any, and from A. These types of structures occur in our everyday's life, that's why we study them in this book.
Book Detail :-
This book has following details information.
Title:
Smarandache Loops by W. B. Vasantha Kandasamy by NA
Publisher:
American Research Press
Series:
eBookDirectory
Year:
2002
Pages:
129
Type:
PDF
Language:
English
ISBN-10 #:
1931233632
ISBN-13 #:
9781931233637
Country:
Pakistan
License:
N\A
Get this book from Amazon
About Author :-
The author NA
NA
Book Contents :-
conver the following topics.
1. General Fundamentals
2. Loops and its properties
3. Smarandache Loops
4. Properties About S-Loops
5. Research Problems
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