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Smarandache Rings

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Smarandache Rings

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Author : W. B. Vasantha Kandasamy
language : en
Publisher: Infinite Study
Release Date : 2002

Smarandache Rings written by W. B. Vasantha Kandasamy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

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 Near Rings

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Author : W. B. Vasantha Kandasamy
language : en
Publisher: Infinite Study
Release Date : 2002

Smarandache Near Rings written by W. B. Vasantha Kandasamy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

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 Near-Ring is a non-empty set N together with two binary operations '+' and '.' such that (N, +) is a group (not necessarily abelian), (N, .) is a semigroup. For all a, b, c in N we have (a + b) . c = a . c + b . c. A Near-Field is a non-empty set P together with two binary operations '+' and '.' such that (P, +) is a group (not necessarily abelian), (P \ {0}, .) is a group. For all a, b, c I P we have (a + b) . c = a . c + b . c. A Smarandache Near-ring is a near-ring N which has a proper subset P in N, where P is a near-field (with respect to the same binary operations on N).

Smarandache Non Associative Rings

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Author : W. B. Vasantha Kandasamy
language : en
Publisher: Infinite Study
Release Date : 2002

Smarandache Non Associative Rings written by W. B. Vasantha Kandasamy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

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 Fuzzy Algebra

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Author : W. B. Vasantha Kandasamy
language : en
Publisher: Infinite Study
Release Date : 2003

Smarandache Fuzzy Algebra written by W. B. Vasantha Kandasamy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

The author studies the Smarandache Fuzzy Algebra, which, like its predecessor Fuzzy Algebra, arose from the need to define structures that were more compatible with the real world where the grey areas mattered, not only black or white.In any human field, a Smarandache n-structure on a set S means a weak structure {w(0)} on S such that there exists a chain of proper subsets P(n-1) in P(n-2) in?in P(2) in P(1) in S whose corresponding structures verify the chain {w(n-1)} includes {w(n-2)} includes? includes {w(2)} includes {w(1)} includes {w(0)}, where 'includes' signifies 'strictly stronger' (i.e., structure satisfying more axioms).This book is referring to a Smarandache 2-algebraic structure (two levels only of structures in algebra) on a set S, i.e. a weak structure {w(0)} on S such that there exists a proper subset P of S, which is embedded with a stronger structure {w(1)}. Properties of Smarandache fuzzy semigroups, groupoids, loops, bigroupoids, biloops, non-associative rings, birings, vector spaces, semirings, semivector spaces, non-associative semirings, bisemirings, near-rings, non-associative near-ring, and binear-rings are presented in the second part of this book together with examples, solved and unsolved problems, and theorems. Also, applications of Smarandache groupoids, near-rings, and semirings in automaton theory, in error correcting codes, and in the construction of S-sub-biautomaton can be found in the last chapter.

Bilagebraic Structures And Smarandache Bialgebraic Structures

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Author : W. B. Vasantha Kandasamy
language : en
Publisher: Infinite Study
Release Date : 2003-01-01

Bilagebraic Structures And Smarandache Bialgebraic Structures written by W. B. Vasantha Kandasamy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.

Generally the study of algebraic structures deals with the concepts like groups, semigroups, groupoids, loops, rings, near-rings, semirings, and vector spaces. The study of bialgebraic structures deals with the study of bistructures like bigroups, biloops, bigroupoids, bisemigroups, birings, binear-rings, bisemirings and bivector spaces. A complete study of these bialgebraic structures and their Smarandache analogues is carried out in this book. For examples: A set (S, +, *) with two binary operations ?+? and '*' is called a bisemigroup of type II if there exists two proper subsets S1 and S2 of S such that S = S1 U S2 and(S1, +) is a semigroup.(S2, *) is a semigroup. Let (S, +, *) be a bisemigroup. We call (S, +, *) a Smarandache bisemigroup (S-bisemigroup) if S has a proper subset P such that (P, +, *) is a bigroup under the operations of S. Let (L, +, *) be a non empty set with two binary operations. L is said to be a biloop if L has two nonempty finite proper subsets L1 and L2 of L such that L = L1 U L2 and(L1, +) is a loop, (L2, *) is a loop or a group. Let (L, +, *) be a biloop we call L a Smarandache biloop (S-biloop) if L has a proper subset P which is a bigroup. Let (G, +, *) be a non-empty set. We call G a bigroupoid if G = G1 U G2 and satisfies the following:(G1 , +) is a groupoid (i.e. the operation + is non-associative), (G2, *) is a semigroup. Let (G, +, *) be a non-empty set with G = G1 U G2, we call G a Smarandache bigroupoid (S-bigroupoid) if G1 and G2 are distinct proper subsets of G such that G = G1 U G2 (neither G1 nor G2 are included in each other), (G1, +) is a S-groupoid.(G2, *) is a S-semigroup.A nonempty set (R, +, *) with two binary operations ?+? and '*' is said to be a biring if R = R1 U R2 where R1 and R2 are proper subsets of R and (R1, +, *) is a ring, (R2, +, ?) is a ring.A Smarandache biring (S-biring) (R, +, *) is a non-empty set with two binary operations ?+? and '*' such that R = R1 U R2 where R1 and R2 are proper subsets of R and(R1, +, *) is a S-ring, (R2, +, *) is a S-ring.

Smarandache Special Definite Algebraic Structures

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Author : W. B. Vasantha Kandasamy
language : en
Publisher: Infinite Study
Release Date : 2009-01-01

Smarandache Special Definite Algebraic Structures written by W. B. Vasantha Kandasamy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-01 with Mathematics categories.

We study these new Smarandache algebraic structures, which are defined as structures which have a proper subset which has a weak structure.A Smarandache Weak Structure on a set S means a structure on S that has a proper subset P with a weaker structure.By proper subset of a set S, we mean a subset P of S, different from the empty set, from the original set S, and from the idempotent elements if any.A Smarandache Strong Structure on a set S means a structure on S that has a proper subset P with a stronger structure.A Smarandache Strong-Weak Structure on a set S means a structure on S that has two proper subsets: P with a stronger structure, and Q with a weaker structure.

Smarandache Function Journal Vol 12 2001

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Author : Charles Ashbacher
language : en
Publisher: Infinite Study
Release Date :

Smarandache Function Journal Vol 12 2001 written by Charles Ashbacher and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

A collection of papers concerning Smarandache type functions, numbers, sequences, inteqer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc.

Smarandache Notions Vol 14

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Author : W. B. Vasantha Kandasamy
language : en
Publisher: Infinite Study
Release Date : 2004-01-01

Smarandache Notions Vol 14 written by W. B. Vasantha Kandasamy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Number theory categories.

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.

Smarandache Notions Vol 12 Proceedings Of The Second International Conference On Smarandache Type Notions In Mathematics And Quantum Physics

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Author : Leonardo Motta
language : en
Publisher: Infinite Study
Release Date : 2001-01-01

Smarandache Notions Vol 12 Proceedings Of The Second International Conference On Smarandache Type Notions In Mathematics And Quantum Physics written by Leonardo Motta and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with categories.

Smarandache Function Journal Vol 14 2004

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Author : Sabin Tabirca
language : en
Publisher: Infinite Study
Release Date :

Smarandache Function Journal Vol 14 2004 written by Sabin Tabirca and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Smarandache Rings

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