Smarandache Loops by W. B. Vasantha Kandasamy

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 :-
Title: Smarandache Loops by W. B. Vasantha Kandasamy
Publisher: American Research Press
Year: 2002
Pages: 129
Type: PDF
Language: English
ISBN-10 #: 1931233632
ISBN-13 #: 9781931233637
License: Linked Content Owned by Author
Amazon: Amazon

About Author :-
The author Dr W. B. Vasantha Kandasamy is an Associate Professor in the Department of Mathematics, Indian Institute of Technology Madras, Chennai. In the past decade she has guided 11 Ph.D. scholars in the different fields of non-associative algebras, algebraic coding theory, transportation theory, fuzzy groups, and applications of fuzzy theory of the problems faced in chemical industries and cement industries. Currently, four Ph.D. scholars are working under her guidance. She has to her credit 636 research papers. She has guided over 51 M.Sc. and M.Tech. projects. She has worked in collaboration projects with the Indian Space Research Organization and with the Tamil Nadu State AIDS Control Society. This is her 29th book. On India's 60th Independence Day, Dr.Vasantha was conferred the Kalpana Chawla Award for Courage and Daring Enterprise by the State Government of Tamil Nadu in recognition of her sustained fight for social justice in the Indian Institute of Technology (IIT) Madras and for her contribution to mathematics. (The award, instituted in the memory of Indian-American astronaut Kalpana Chawla who died aboard Space Shuttle Columbia). The award carried a cash prize of five lakh rupees (the highest prize-money for any Indian award) and a gold medal.

Book Contents :-
1. General Fundamentals 2. Loops and its properties 3. Smarandache Loops 4. Properties About S-Loops 5. Research Problems

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