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This is Smarandache's Russian translation from Romanian on Algebra.

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...Ion GOlAN Ralsa GRIGOR Vasile MARIN Aorentm SMARANDACHE P I . f • • 1 Algebra In exerc;lii 1; probleme pentru liceu • , II /(11- "., ,., • ...

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...Prezenta lucrare contine exercitii §i probleme de algebra, grupate pe capitole, pentru clasele superioare de licee §i §coli medii de cultura generala. Scopul ei este pregatirea matematica a elevilor din liceele de toate categoriile §i va fi utila in lucrul de sine statator...

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...Ion GOlAN Ralsa GRIGOR Vasile MARIN Aorentm SMARANDACHE P I . f • • 1 Algebra In exerc;lii 1; probleme pentru liceu • , II /(11- "., ,., • ... ...f.- II J ;.\ Ion GOlAN Raisa GRIGOR Vasile MARIN Florentin SMARANDACHE Algebra in exerciJii Ii probleme pentru liceu Mulfimi, operafii cu mulfi... ... Ot~iniiu: bd. Mircea cel Batrin, Dr. 9, sectoml Ciocana. Tel.: 34 64 61. ALGEBRA IN EXEROTII $1 PROBLEME PENTRU LICEU (Multimi, operatii cu multimi... ...-040-2 Cuvant inainte Prezenta lucrare contine exercitii §i probleme de algebra, grupate pe capitole, pentru clasele superioare de licee §i §coli ... ... - X. - Bucure§ti: Editura didactica §i pedagogica, 1978. 4. Militaru C. "Algebra", Exercilii §i probleme pentru liceu §i admitere in fa­ cuItate. - ... ...tura "Alux" S.R.L, 1992. 5. Nifstifsescu C., Nita C., Popa S. Matematidi "Algebra", manual pentru clasa X-a. - Bucure§ti: Editura didactica §i pedag... ... Editura tehnica, 1963. 8. Stamate 1., Stoian 1. Culegere de probleme de algebra pentru licee. - Bu­ cure§ti: Editura didactica §i pedagogica, 1971.... ...atura romana, ~olile alalingve. Bacalaureat Vasile Marin (coordonator) - Algebra. Ecuatii ?i inecuatii. Vol. I. Bacalaureat Muzica. Manual pentru ...

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... n-linear functionals. The final chapter suggests over a hundred problems. It is important that the reader should be well versed with not only linear algebra but also n-linear algebras of type I....

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...This book has four chapters. The first chapter just introduces n-group which is essential for the definition of n-vector spaces and n-linear algebras of type I. Chapter two gives the notion of n-vector spaces and several related results which are analogues of the classical linear algebra theorems. In case of n-vector spaces we can define several types of linear tr...

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...Preface 5 Chapter One BASIC CONCEPTS 7 Chapter Two n-VECTOR SPACES OF TYPE I AND THEIR PROPERTIES 13 Chapter Three APPLICATIONS OF n-LINEAR ALGEBRA OF TYPE I 81 Chapter Four SUGGESTED PROBLEMS 103 FURTHER READING 111 INDEX 116 ABOUT THE AUTHORS 120...

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...This paper contains exercises and problems of algebra and grouped chapters, the upper classes of secondary schools and coli culture media general. Its purpose is to prepare students from high schools mathematics categories and will be helpful in working independently. Al...

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...In this book, we study the subject of Smarandache Fuzzy Algebra. Originally, the revolutionary theory of Smarandache notions was born as a paradoxist movement that challenged the status quo of existing mathematics. The genesis of Smarandache Notions, a field founded by Florentine ...

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...w. b. vasantha kandasamy SMARANDACHE FUZZY ALGEBRA AMERICAN RESEARCH PRESS ... ... semi group groupoid group loop 1 SMARANDACHE FUZZY ALGEBRA W. B. Vasantha Kandasamy Department of Mathematics... ...ture on the cover is a simple graphic illustration depicting the classical algebraic structures with single binary operations and their Smarandache a... ...ft, composed of concentric circles, depicts the traditional conception of algebraic structures, and the pictures of the right, with their liberal in... ...ures of the right, with their liberal intersections, describe Smarandache algebraic structures. In fact, Smarandache Algebra, like its predecessor, ... ...aic structures. In fact, Smarandache Algebra, like its predecessor, Fuzzy Algebra, arose from the need to define structures which were more compatib... ...ca 3 CONTENTS Preface 5 PART ONE 1. SOME RESULTS ON FUZZY ALGEBRA 1.1 Fuzzy subsets 9 1.2 Groups and fuzzy subgroups 11 1.3 Fuzz... ...upoids and its generalizations 144 1.12 Miscellaneous properties in Fuzzy Algebra 187 PART TWO 2. SMARANDACHE FUZZY SEMIGROUPS AND ITS PROPE... ...ar-rings 389 6.4 Problems 398 7. APPLICATIONS OF SMARANDACHE FUZZY ALGEBRAIC STRUCTURES 7.1 Applications of Smarandache algebraic struct...

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...This book has six chapters. First chapter is introductory in nature. The new concept of non-associative semi-linear algebras is introduced in chapter two. This structure is built using groupoids over semi-fields. Third chapter introduces the notion of non-associative linear algebras. These algebraic structures are built using the new class...

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...e resultant product may not be a loop in general. For the concept of semifield refer [41]. We will be using these loops and groupoids to build linear algebra and semilinear algebras which are non associative. ...

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...Preface 5 Chapter One BASIC CONCEPTS 7 Chapter Two NON ASSOCIATIVE SEMILINEAR ALGEBRAS 13 Chapter Three NON ASSOCIATIVE LINEAR ALGEBRAS 83 Chapter Four GROUPOID VECTOR SPACES 111 Chapter Five APPLICATION OF NON ASSOCIATIVE VECTOR SPACES / LINEAR ALGEBRAS 161 Chapter Six SUGGESTED PROBLEMS 16...

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...make use of the literature in case the reader is not thorough with the basics. The second chapter deals with different types of neutrosophic bilinear algebras and bivector spaces and proves several results analogous to linear bialgebra. In chapter three the authors introduce the notion of n-linear algebras and prove several theorems related to them. Many of the classical t...

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...Dedication 5 Preface 7 Chapter One INTRODUCTION TO BASIC CONCEPTS 9 1.1 Introduction to Bilinear Algebras and their Generalizations 9 1.2 Introduction to Neutrosophic Algebraic Structures 11 Chapter Two NEUTROSOPHIC LINEAR ALGEBRA 15 2.1 Neutrosophic Bivector Spaces 15 2.2 Strong Neutrosophic Bivector Spaces 32 2....

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...ain motivation and desire for writing this book, is the direct appreciation and attraction towards the Smarandache notions in general and Smarandache algebraic structures in particular. The Smarandache semigroups exhibit properties of both a group and a semigroup simultaneously. This book is a piece of work on Smarandache semigroups and assumes the reader to have a good ba...

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...tion and attraction towards the Smarandache notions in general and Smarandache algebraic structures in particular. The Smarandache semigroups exhibi... ...semigroups. 6 The final chapter, a special attraction to researchers and algebraists is a list of open research problems. Most of the propose... ...Conference on Combinatorial Methods in Mathematics, II Meeting of the project 'Algebra, Geometria e Combinatoria', Faculdade de Ciencias da Univ... ... Universidade do Porto, Portugal, 9-11 July 1998. 2. R. Padilla, Smarandache Algebraic Structures, Smarandache Notions Journal, USA, Vol.9, No. 1... ...ions Journal, USA, Vol.9, No. 1-2, 36-38, (1998). 3. R. Padilla. Smarandache Algebraic Structures, Bulletin of Pure and Applied Sciences, Delhi, ... ...tp://www.gallup.unm.edu/~smarandache/ALG-S-TXT.TXT 4. F. Smarandache, Special Algebraic Structures, in Collected Papers, Vol. III, ... ...his book. Thus, the main purpose of this book is to make both researcher and an algebraist to know and enjoy the Smarandache analog concept for group... ... concept for groups. It is pertinent to mention that Smarandache notions on all algebraic and mathematical structures are interesting to the world o... ...es for a lucid extension of the Cayley's theorem. This book deals only with the algebraic structure of groups in the context of Smarandache structur...

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...matician George Boole. She was the author of several works on teaching and teaching mathematics in particular. This short book, Philosophy and Fun of Algebra, is meant to be read by children and introduces algebra and logic. She uses the word “algebra” broadly, defining it as a “method of solving problems by honest confession of one’s ignorance”. Using this definition, Boo...

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...The algebraic structure, linear algebra happens to be one of the subjects which yields itself to applications to several fields like coding or communication theory, Markov chains, representation of groups and graphs, Leontief eco...

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...In this section we give the definition of linear algebra and just state the few important theorems like Cayley Hamilton theorem, Cyclic Decomposition Theorem, Generalized Cayley Hamilton Theorem and give some properties about linear algebra....

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...NTENTS Preface 5 Chapter One INTRODUCTION TO LINEAR ALGEBRA AND S- LINEAR ALGEBRA 1.1 Basic properties of linear algebra ... ... 1.1 Basic properties of linear algebra 7 1.2 Introduction to s-linear algebra 15 1.3 Some aapplications of S-linear algebra 30 Chapter... ...PHIC LINEAR BIALGEBRA AND ITS APPLICATION 4.1 Some basic neutrosophic algebraic structures 131 4.2 Smarandache neutrosophic linear bialgebr... ... INDEX 229 ABOUT THE AUTHORS 238 5 Preface The algebraic structure, linear algebra happens to be one of the subjects whi... ...omic models and so on. This book has for the first time, introduced a new algebraic structure called linear bialgebra, which is also a very powerfu... ...algebraic structure called linear bialgebra, which is also a very powerful algebraic tool that can yield itself to applications. With the recent i... ...ache neutrosophic linear bialgebra and also give the applications of these algebraic structures. It is important to mention here it is a matter of... ...mention here it is a matter of simple exercise to extend these to linear n-algebra for any n greater than 2; for n = 2 we get the linear bialgebra. ... ...pters. In the first chapter we just introduce some basic notions of linear algebra and S- linear algebra and their applications. Chapter two introduc...

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...This book has eight chapters. The first chapter is introductory in nature. Polynomials with matrix coefficients are introduced in chapter two. Algebraic structures on these polynomials with matrix coefficients is defined and described in chapter three. Chapter four introduces natural product on matrices. Natural product on super matrices is introduced in chapter fiv...

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...ion sequence which is a new concept, related sequences, conjectures, properties, and problems. This study was conducted by using (Maple 8){a computer Algebra System. Keywords Smarandache inversion, Smarandache reverse sequence. Introduction In [1], C.Ashbacher, studied the Smarandache reverse sequence: 1; 21; 321; 4321; 54321; 654321; 7654321; 87654321; 987654321; 10...

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...the Smarandache-type function 31 P. Zhang : An equation involving the function ±k(n) 35 Y. B. Jun : Smarandache fantastic ideals of Smarandache BCI-algebras 40 T. Jayeo. la : On the Universality of some Smarandache loops of Bol-Moufang type 45 W. Kandasamy, M. Khoshnevisan and K. Ilanthenral : Smarandache representation and its applications 59 Y. Wang, X. Ren and S. M...

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...ures and their duals. The final chapter gives problems for the interested reader to solve. Our main motivation is to attract more researchers towards algebra and its various applications....

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...1.1 Groups, N-group and their basic Properties It is a well-known fact that groups are the only algebraic structures with a single binary operation that is mathematically so perfect that an introduction of a richer structure within it is impossible. Now we proceed on to define a group. DEFINITION 1.1.1: A non empty set...

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...ps, N-group and their basic Properties 7 1.2 Semigroups and N-semigroups 11 1.3 Loops and N-loops 12 1.4 Groupoids and N-groupoids 25 1.5 Mixed N-algebraic Structures 32 Chapter Two NEUTROSOPHIC GROUPS AND NEUTROSOPHIC N-GROUPS 2.1 Neutrosophic Groups and their Properties 40 2.2 Neutrosophic Bigroups and their Properties 52 2.3 Neutrosophic N-groups and their Pro...

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...lated to Hexagon-numbers 16 X. Ren, etc. : A structure theorem of right C-rpp semigroups 21 A. R. Gilani and B. N. Waphare : Fuzzy extension in BCI-algebras 26 A. S. Shabani : The Pell's equation x2 ¡ Dy2 = §a 33 L. Cheng : On the mean value of the Smarandache LCM function 41 W. Guan : Four problems related to the Pseudo-Smarandache-Squarefree function 45 Y. Lou : On...