Smarandache

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Smarandache Rings

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233640
Total Pages : 222 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Smarandache Rings by : W. B. Vasantha Kandasamy

Download or read book Smarandache Rings written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2002 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 two particular cases:A Smarandache ring of level I (S-ring I) is a ring R that contains a proper subset that is a field with respect to the operations induced. A Smarandache ring of level II (S-ring II) is a ring R that contains a proper subset A that verifies: ?A is an additive abelian group; ?A is a semigroup under multiplication;?For a, b I A, a?b = 0 if and only if a = 0 or b = 0.

Smarandache Semigroups

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233594
Total Pages : 95 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Smarandache Semigroups by : W. B. Vasantha Kandasamy

Download or read book Smarandache Semigroups written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2002-12-01 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 in A which is embedded with a stronger structure S.These types of structures occur in our everyday life, that?s why we study them in this book.Thus, as a particular case:A Smarandache Semigroup is a semigroup A which has a proper subset B in A that is a group (with respect to the same binary operation on A).

The Math Encyclopedia of Smarandache type Notions

Author : Marius Coman
Publisher : Infinite Study
ISBN 13 : 1599732521
Total Pages : 136 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis The Math Encyclopedia of Smarandache type Notions by : Marius Coman

Download or read book The Math Encyclopedia of Smarandache type Notions written by Marius Coman and published by Infinite Study. This book was released on with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: About the works of Florentin Smarandache have been written a lot of books (he himself wrote dozens of books and articles regarding math, physics, literature, philosophy). Being a globally recognized personality in both mathematics (there are countless functions and concepts that bear his name) and literature, it is natural that the volume of writings about his research is huge. What we try to do with this encyclopedia is to gather together as much as we can both from Smarandache’s mathematical work and the works of many mathematicians around the world inspired by the Smarandache notions. We structured this book using numbered Definitions, Theorems, Conjectures, Notes and Comments, in order to facilitate an easier reading but also to facilitate references to a specific paragraph. We divided the Bibliography in two parts, Writings by Florentin Smarandache (indexed by the name of books and articles) and Writings on Smarandache notions (indexed by the name of authors). We treated, in this book, about 130 Smarandache type sequences, about 50 Smarandache type functions and many solved or open problems of number theory. We also have, at the end of this book, a proposal for a new Smarandache type notion, id est the concept of “a set of Smarandache-Coman divisors of order k of a composite positive integer n with m prime factors”, notion that seems to have promising applications, at a first glance at least in the study of absolute and relative Fermat pseudoprimes, Carmichael numbers and Poulet numbers. This encyclopedia is both for researchers that will have on hand a tool that will help them “navigate” in the universe of Smarandache type notions and for young math enthusiasts: many of them will be attached by this wonderful branch of mathematics, number theory, reading the works of Florentin Smarandache.

Smarandache Loops

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233632
Total Pages : 129 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Smarandache Loops by : W. B. Vasantha Kandasamy

Download or read book Smarandache Loops written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2002 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.As an example:A non-empty set L is said to form a loop, if on L is defined a binary operation called product, denoted by '?', such that:?For all a, b I L we have a ? b I L (closure property);?There exists an element e I L such that a ? e = e ? a = a for all a I L (e is the identity element of L);?For every ordered pair (a, b) I L ' L there exists a unique pair (x, y) in L such that ax = b and ya = b.Whence:A Smarandache Loop (or S-loop) is a loop L such that a proper subset M of L is a subgroup (with respect to the same induced operation).

SMARANDACHE NUMBERS REVISITED

Author : A.A.K. MAJUMDAR
Publisher : Infinite Study
ISBN 13 : 1599735733
Total Pages : 132 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis SMARANDACHE NUMBERS REVISITED by : A.A.K. MAJUMDAR

Download or read book SMARANDACHE NUMBERS REVISITED written by A.A.K. MAJUMDAR and published by Infinite Study. This book was released on with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: More than seven years ago, my first book on some of the Smarandache notions was published. The book consisted of five chapters, and the topics covered were as follows : (1) some recursive type Smarandache sequences, (2) Smarandache determinant sequences, (3) the Smarandache function, (4) the pseudo Smarandache function, and (5) the Smarandache function related and the pseudo Smarandache function related triangles. Since then, new and diversified results have been published by different researchers. The aim of this book to update some of the contents of my previous book, and add some new results.

Linear Algebra and Smarandache Linear Algebra

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233756
Total Pages : 175 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Linear Algebra and Smarandache Linear Algebra by : W. B. Vasantha Kandasamy

Download or read book Linear Algebra and Smarandache Linear Algebra written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2003 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the author analyzes the Smarandache linear algebra, and introduces several other concepts like the Smarandache semilinear algebra, Smarandache bilinear algebra and Smarandache anti-linear algebra. We indicate that Smarandache vector spaces of type II will be used in the study of neutrosophic logic and its applications to Markov chains and Leontief Economic models ? both of these research topics have intense industrial applications. The Smarandache linear algebra, is defined to be a Smarandache vector space of type II, on which there is an additional operation called product, such that for all a, b in V, ab is in V.The Smarandache vector space of type II is defined to be a module V defined over a Smarandache ring R such that V is a vector space over a proper subset k of R, where k is a field.

Comments and Topics on Smarandache Notions and Problems

Author : Kenichiro Kashihara
Publisher : Infinite Study
ISBN 13 : 1879585553
Total Pages : 51 pages
Book Rating : 4.8/5 (795 download)

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Book Synopsis Comments and Topics on Smarandache Notions and Problems by : Kenichiro Kashihara

Download or read book Comments and Topics on Smarandache Notions and Problems written by Kenichiro Kashihara and published by Infinite Study. This book was released on 1996 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Smarandache Notions, Vol. 14

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233799
Total Pages : 418 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Smarandache Notions, Vol. 14 by : W. B. Vasantha Kandasamy

Download or read book Smarandache Notions, Vol. 14 written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2004-01-01 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers concerning any of the Smarandache type functions, sequences, numbers, algorithms, inferior/superior f-parts, magic squares, palindromes, functional iterations, semantic paradoxes, Non-Euclidean geometries, manifolds, conjectures, open problems, algebraic structures, neutrosophy, neutrosophic logic/set/probability, hypothesis that there is no speed barrier in the universe, quantum paradoxes, etc. have been selected for this volume. Contributors are from Australia, China, England, Germany, India, Ireland, Israel, Italy, Japan, Malaysia, Morocco, Portugal, Romania, Spain, USA. Most of the papers are in English, a few of them are in Spanish, Portuguese, or German.

Generalized Partitions and New Ideas on Number Theory and Smarandache Sequences

Author : Amarnath Murthy
Publisher : Infinite Study
ISBN 13 : 1931233349
Total Pages : 219 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Generalized Partitions and New Ideas on Number Theory and Smarandache Sequences by : Amarnath Murthy

Download or read book Generalized Partitions and New Ideas on Number Theory and Smarandache Sequences written by Amarnath Murthy and published by Infinite Study. This book was released on 2005-01-01 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Florentin Smarandache is an incredible source of ideas, only some of which are mathematical in nature. Amarnath Murthy has published a large number of papers in the broad area of Smarandache Notions, which are math problems whose origin can be traced to Smarandache. This book is an edited version of many of those papers, most of which appeared in Smarandache Notions Journal, and more information about SNJ is available at http://www.gallup.unm.edu/~smarandache/ . The topics covered are very broad, although there are two main themes under which most of the material can be classified. A Smarandache Partition Function is an operation where a set or number is split into pieces and together they make up the original object. For example, a Smarandache Repeatable Reciprocal partition of unity is a set of natural numbers where the sum of the reciprocals is one. The first chapter of the book deals with various types of partitions and their properties and partitions also appear in some of the later sections.The second main theme is a set of sequences defined using various properties. For example, the Smarandache n2n sequence is formed by concatenating a natural number and its double in that order. Once a sequence is defined, then some properties of the sequence are examined. A common exploration is to ask how many primes are in the sequence or a slight modification of the sequence. The final chapter is a collection of problems that did not seem to be a precise fit in either of the previous two categories. For example, for any number d, is it possible to find a perfect square that has digit sum d? While many results are proven, a large number of problems are left open, leaving a great deal of room for further exploration.

Smarandache Non-Associative Rings

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233691
Total Pages : 151 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Smarandache Non-Associative Rings by : W. B. Vasantha Kandasamy

Download or read book Smarandache Non-Associative Rings written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2002 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 in A which is embedded with a stronger structure S. These types of structures occur in our everyday's life, that's why we study them in this book. Thus, as a particular case: A Non-associative ring is a non-empty set R together with two binary operations '+' and '.' such that (R, +) is an additive abelian group and (R, .) is a groupoid. For all a, b, c in R we have (a + b) . c = a . c + b . c and c . (a + b) = c . a + c . b. A Smarandache non-associative ring is a non-associative ring (R, +, .) which has a proper subset P in R, that is an associative ring (with respect to the same binary operations on R).

Smarandache pseudo-CI algebras

Author : L. C. Ciungu
Publisher : Infinite Study
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4./5 ( download)

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Book Synopsis Smarandache pseudo-CI algebras by : L. C. Ciungu

Download or read book Smarandache pseudo-CI algebras written by L. C. Ciungu and published by Infinite Study. This book was released on 2022-01-01 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we define the notion of Smarandache pseudo-CI algebras and we investigate their properties. We also define and study the notions of Smarandache filters, pseudo-CI Smarandache homomorphisms and modal Smarandache operators on pseudo-CI algebras. The classes of Smarandache fantastic, implicative and positive implicative filters of Smarandache pseudo-CI algebras are defined and studied by extending some results regarding Smarandache fantastic, fresh and clean ideals in Smarandache BCI-algebras and Smarandache BCH-algebras to the case of Smarandache pseudo-CI algebras. The notion of Smarandache commutative pseudo-CI algebras is defined and a characterization theorem is given. It is proved that in the case of commutative Q-Smarandache pseudo-CI algebras the notions of Smarandache filters and fantastic filters coincide.

Collection of Problems on Smarandache Notions

Author : Charles Ashbacher
Publisher : Infinite Study
ISBN 13 : 1879585502
Total Pages : 75 pages
Book Rating : 4.8/5 (795 download)

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Book Synopsis Collection of Problems on Smarandache Notions by : Charles Ashbacher

Download or read book Collection of Problems on Smarandache Notions written by Charles Ashbacher and published by Infinite Study. This book was released on 1996 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Smarandache Function Journal, vol. 14/2004

Author : Sabin Tabirca
Publisher : Infinite Study
ISBN 13 :
Total Pages : 418 pages
Book Rating : 4./5 ( download)

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Book Synopsis Smarandache Function Journal, vol. 14/2004 by : Sabin Tabirca

Download or read book Smarandache Function Journal, vol. 14/2004 written by Sabin Tabirca and published by Infinite Study. This book was released on with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of papers concerning Smarandache type functions, numbers, sequences, inteqer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc.

Wandering in the World of Smarandache Numbers

Author : A. A. K. Majumdar
Publisher : Infinite Study
ISBN 13 : 159973124X
Total Pages : 217 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Wandering in the World of Smarandache Numbers by : A. A. K. Majumdar

Download or read book Wandering in the World of Smarandache Numbers written by A. A. K. Majumdar and published by Infinite Study. This book was released on 2010 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers only a part of the wide and diverse field of the Smarandache Notions, andcontains some of the materials that I gathered as I wandered in the world of Smarandache. Mostof the materials are already published in different journals, but some materials are new andappear for the first time in this book. All the results are provided with proofs._ Chapter 1 gives eleven recursive type Smarandache sequences, namely, the SmarandacheOdd, Even, Prime Product, Square Product (of two types), Higher Power Product (of twotypes), Permutation, Circular, Reverse, Symmetric and Pierced Chain sequences_ Chapter 2 deals with the Smarandache Cyclic Arithmetic Determinant and BisymmetricArithmetic Determinant sequences, and series involving the terms of the Smarandachebisymmetric determinant natural and bisymmetric arithmetic determinant sequences_ Chapter 3 treats the Smarandache function S(n)_ Chapter 4 considers, in rather more detail, the pseudo Smarandache function Z(n)_ And the Smarandache S-related and Z-related triangles are the subject matter of Chapter 5.To make the book self-contained, some well-known results of the classical Number Theory aregiven in Chapter 0. In order to make the book up-to-date, the major results of other researchersare also included in the book.At the end of each chapter, several open problems are given.

Groupoids and Smarandache Groupoids

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233616
Total Pages : 115 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Groupoids and Smarandache Groupoids by : W. B. Vasantha Kandasamy

Download or read book Groupoids and Smarandache Groupoids written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2002-12-01 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: Definition: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 in A which is embedded with a stronger structure S.These types of structures occur in our everyday life, that?s why we study them in this book.Thus, as a particular case:A Smarandache Groupoid is a groupoid G which has a proper subset S in G such that S under the operation of G is a semigroup.

Smarandache Notions, Vol. 9

Author : C. Dumitrescu
Publisher : Infinite Study
ISBN 13 : 1879585693
Total Pages : 158 pages
Book Rating : 4.8/5 (795 download)

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Book Synopsis Smarandache Notions, Vol. 9 by : C. Dumitrescu

Download or read book Smarandache Notions, Vol. 9 written by C. Dumitrescu and published by Infinite Study. This book was released on 2000-08-01 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:

n-Fold Filters in Smarandache Residuated Lattices, Part I

Author : Somayeh Motamed
Publisher : Infinite Study
ISBN 13 :
Total Pages : 12 pages
Book Rating : 4./5 ( download)

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Book Synopsis n-Fold Filters in Smarandache Residuated Lattices, Part I by : Somayeh Motamed

Download or read book n-Fold Filters in Smarandache Residuated Lattices, Part I written by Somayeh Motamed and published by Infinite Study. This book was released on with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we introduce the notions of n-fold BL-Smarandache positive implicative filter and n-fold BL-Smarandache implicative filter in Smarandache residuated lattices and study the relations among them. And we also introduce the notions of n-fold Smarandache positive implicateve BL-residuated lattice, n-fold Smarandache implicateve BL-residuated lattice and investigate its properties.