Smarandache Semirings, Semifields and Semivector Spaces by W. B. Vasantha Kandasamy
Share this page:-
We need Your Support, Kindly Share this Web Page with Other Friends
Congratulations, the link is avaliable for free download.
About this book :-
Kandasamy explores some special types of mathematical structures. These are based on the idea that a large system may contain a smaller part that is more structured or follows stronger rules. For example, a Smarandache semiring is a type of number system where a smaller part inside it behaves like a semifield (a structure where you can divide numbers, except by zero). Similarly, a Smarandache semifield contains a smaller part that acts like a semi-algebra, which means it also supports scalar multiplication like in algebra. The book also defines Smarandache semivector spaces, which are similar to vector spaces but may not have all the usual properties—though a part of them does. In short, the book studies mathematical systems that are not perfect everywhere, but have pockets of stronger, well-behaved structures inside. This approach is useful in creating flexible systems that still contain useful, powerful components.
Smarandache notions, which can be undoubtedly characterized as interesting mathematics, has the capacity of being utilized to analyse, study and introduce, naturally, the concepts of several structures by means of extension or identification as a substructure. Several researchers around the world working on Smarandache notions have systematically carried out this study. This is the first book on the Smarandache algebraic structures that have two binary operations.
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 every day's life, that's why we study them in this book. Thus, as three particular cases: 1) A Smarandache semiring is a semiring A such that a proper subset B of A is a semifield (with respect to the same induced operation). 2) A Smarandache semifield is a semifield A such that a proper subset B of A is a k-semi algebra, with respect to the same induced operations and an external operator. 3) A Smarandache semivector space is a semivector space A (over a semifield B) which is a Smarandache semigroup.
Semirings are algebraic structures with two binary operations enjoying several properties and it is the most generalized structure — for all rings and fields are semirings. The study of this concept is very meagre except for a very few research papers. Now, when we study the Smarandache semirings (S-semiring), we make the richer structure of semifield to be contained in an S-semiring; and this S-semiring is of the first level. To have the second level of S-semirings, we need a still richer structure, viz. field to be a subset in a S-semiring. This is achieved by defining a new notion called the Smarandache mixed direct product. Likewise we also define the Smarandache semifields of level II. This study makes one relate, compare and contrasts weaker and stronger structures of the same set.
Book Detail :-
This book has following details information.
Title:
Smarandache Semirings, Semifields and Semivector Spaces by W. B. Vasantha Kandasamy by NA
Publisher:
American Research Press
Series:
eBookDirectory
Year:
2002
Pages:
122
Type:
PDF
Language:
English
ISBN-10 #:
1931233624
ISBN-13 #:
9781931233620
Country:
Pakistan
License:
N\A
Get this book from Amazon
About Author :-
The author NA
NA
Book Contents :-
conver the following topics.
1. Preliminary Notions
2. Semirings and its Properties
3. Semifields and Semivector Spaces
4. Smarandache Semirings
5. Smarandache Semifields
6. Smarandache Semivector Spaces and Its Properties
7. Research Problems
Note :-
We are not the owner of this book/notes. We provide it which is already avialable on the internet. For any further querries please contact us. We never SUPPORT PIRACY. This copy was provided for students who are financially troubled but want studeing to learn.
If You Think This Materials Is Useful, Please get it legally from the PUBLISHERS.
Thank you.
Now please OPEN for DOWNLOAD the BOOK.
'
Similar
Abstract Algebra
Books
|
A Computational Introduction to Number Theory & Algebra
This textbook that introduces number theory and algebra with a focus on computational methods and real-world applications, particularly in cryptography and coding theory. Designed for students in computer science or mathematics, the book requires min . . . READ MORE
|
|
|
Topological Groups: Yesterday, Today, Tomorrow - Morris
This text offering a comprehensive overview of topological group theory. It traces the field's development from foundational questions posed by David Hilbert in 1900 to contemporary research.
It required half a century of effort by several generati . . . READ MORE
|
|
|
Algebraic Topology by Allen Hatcher
Allen Hatcher's Algebraic Topology is a widely used textbook that introduces the field of algebraic topology. In most major universities it's often used in graduate-level courses and is appreciated for its clear, geometric approach.
This introductor . . . READ MORE
|
|
|
Model Theory, Algebra, and Geometry by Deirdre Haskell
Model theory is a branch of mathematical logic that has found applications in several areas of algebra and geometry. This text explores how model theory applies to various areas of algebra and geometry. The book demonstrates how abstract concepts in . . . READ MORE
|
|
|
Modeling, Functions, and Graphs: Algebra for College
This book is a comprehensive algebra textbook designed for college students. It focus on three core themes throughout their textbook: Modeling, Functions, Graphs and motivate students to acquire the skills and techniques of algebra by placing them in . . . READ MORE
|
|