Smarandache Non Associative Rings

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233691
Total Pages : 151 pages
Book Rating : 4.99/5 ( download)

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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).

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233799
Total Pages : 418 pages
Book Rating : 4.98/5 ( download)

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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.

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233713
Total Pages : 272 pages
Book Rating : 4.12/5 ( download)

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Download or read book Bilagebraic Structures and Smarandache Bialgebraic Structures written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2003-01-01 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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

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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.

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233748
Total Pages : 455 pages
Book Rating : 4.43/5 ( download)

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Download or read book Smarandache Fuzzy Algebra written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2003 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233667
Total Pages : 201 pages
Book Rating : 4.68/5 ( download)

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Download or read book Smarandache Near-Rings written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2002 with total page 201 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 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).

Author : Zhang Wenpeng
Publisher : Infinite Study
ISBN 13 : 1599730022
Total Pages : 203 pages
Book Rating : 4.28/5 ( download)

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Download or read book Scientia Magna, Vol. 1, No. 2, 2005 written by Zhang Wenpeng and published by Infinite Study. This book was released on 2006 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collection of papers from various scientists dealing with smarandache notions in science.

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1599732254
Total Pages : 209 pages
Book Rating : 4.51/5 ( download)

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Download or read book Subset Non Associative Semirings written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Wenpeng Zhang
Publisher : Infinite Study
ISBN 13 : 1599731274
Total Pages : 151 pages
Book Rating : 4.78/5 ( download)

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Download or read book Proceedings of the Sixth International Conference on Number Theory and Smarandache Notions written by Wenpeng Zhang and published by Infinite Study. This book was released on 2010 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Book is devoted to the proceedings of the Sixth International Conferenceon Number Theory and Smarandache Notions held in Tianshui during April 24-25,2010. The organizers were Prof. Zhang Wenpeng and Prof. Wangsheng He from Tianshui Normal University. The conference was supported by Tianshui Normal University and there were more than 100 participants.

Author : W. B. Vasantha Kandasamy, Florentin Smarandache
Publisher : Infinite Study
ISBN 13 : 1599731762
Total Pages : 233 pages
Book Rating : 4.66/5 ( download)

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Download or read book Non Associative Linear Algebras written by W. B. Vasantha Kandasamy, Florentin Smarandache and published by Infinite Study. This book was released on 2012 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: