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.

Download or read book SMARANDACHE SOFT GROUPOIDS written by Mumtaz Ali and published by Infinite Study. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, Smarandache soft groupoids shortly (SS-groupoids) are introduced as a generalization of Smarandache Soft semigroups (SS-semigroups) . A Smarandache Soft groupoid is an approximated collection of Smarandache subgroupoids of a groupoid. Further, we introduced parameterized Smarandache groupoid and strong soft semigroup over a groupoid Smarandache soft ideals are presented in this paper. We also discussed some of their core and fundamental properties and other notions with sufficient amount of examples. At the end, we introduced Smarandache soft groupoid homomorphism.

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).

Download or read book Subset Interval Groupoids written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Groupoids of Type I and II Using 0 n written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2014 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Study of algebraic structures built using [0, n) looks to be one of interesting and innovative research. Here we define two types of groupoids using [0, n), both of them are of infinite order. It is an open conjecture to find whether this new class of groupoids satisfy any of the special identities like Moufang identity or Bol identity and so on.

Download or read book Interval Groupoids written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2010 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book defines new classes of groupoids, like matrix groupoid, polynomial groupoid, interval groupoid, and polynomial groupoid.An interesting feature of this book is that introduces 77 new definitions substantiated and described by 426 examples and 150 theorems.

Download or read book Subset Groupoids written by W. B. Vasantha Kandasamy, Florentin Smarandache and published by Infinite Study. This book was released on 2013 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Scientia Magna Vol 6 No 1 2010 written by Zhang Wenpeng and published by Infinite Study. This book was released on 2010 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers on Smarandache¿s codification used in computer programming, smarandacheials, totient and congruence functions, sequences, irrational constants in number theory, multi-space and geometries.

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.

Download or read book Generalized Fibonacci sequences in groupoids written by Hee Sik Kim and published by Infinite Study. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we introduce the notion of generalized Fibonacci sequences over a groupoid and discuss it in particular for the case where the groupoid contains idempotents and pre-idempotents. Using the notion of Smarandache-type P-algebra, we obtain several relations on groupoids which are derived from generalized Fibonacci sequences.

Download or read book N Algebraic Structures written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2005-01-01 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, for the first time we introduce the notions of N-groups, N-semigroups, N-loops and N-groupoids. We also define a mixed N-algebraic structure. The book is organized into six chapters. The first chapter gives the basic notions of S-semigroups, S-groupoids and S-loops thereby making the book self-contained. Chapter two introduces N-groups and their Smarandache analogues. In chapter three, N-loops and Smarandache N-loops are introduced and analyzed. Chapter four defines N-groupoids and S-N-groupoids. Since the N-semigroup structures are sandwiched between groups and groupoids, the study can be carried out without any difficulty. Mixed N-algebraic structures and S-mixed algebraic structures are given in chapter five. Some problems are suggested in chapter six. It is pertinent to mention that several exercises and problems (Some in the form of proof to the theorems are given in all the chapters.) A reader who attempts to solve them will certainly gain a sound knowledge about these concepts. We have given 50 problems for the reader to solve in chapter 6. The main aim of this book is to introduce new concepts and explain them with examples there by encouraging young mathematics to pursue research in this direction. Several theorems based on the definition can be easily proved with simple modification. Innovative readers can take up that job. Also these notions find their applications in automaton theory and coloring problems. The N-semigroups and N-automaton can be applied to construct finite machines, which can perform multitasks, so their capability would be much higher than the usual automaton of finite machines constructed. We have suggested a list of references for further reading.

Download or read book Graphs as Groups written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2009 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the first time, every finite group is represented in the form of a graph in this book. This study is significant because properties of groups can be immediately obtained by looking at the graphs of the groups.

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.

Download or read book Smarandache Neutrosophic Algebraic Structures written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2006-01-01 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Smarandache algebraic structures that inter-relates two distinct algebraic structures and analyzes them relatively can be considered a paradigm shift in the study of algebraic structures. For instance, the algebraic structure Smarandache semigroup simultaneously involves both group and semigroup.Recently, Neutrosophic Algebraic Structures were introduced. This book ventures to define Smarandache Neutrosophic Algebraic Structures.Here, Smarandache neutrosophic structures of groups, semigroups, loops and groupoids and their N-ary structures are introduced and analyzed. There is a lot of scope for interested researchers to develop these concepts.

Download or read book Non Associative Algebraic Structures Using Finite Complex Numbers written by W.B. Vasantha Kandasamy, Florentin Smarandache and published by Infinite Study. This book was released on 2012 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors have used the concept of finite complex modulo integers to construct non associative algebraic structures like groupoids, loops and quasi-loops.Using these structures we built non associative complex matrix groupoids and complex polynomial groupoids.The authors suggest over 300 problems and some are at the research level.

Download or read book Smarandache n Structure on CI Algebras written by Arsham Borumand Saeid and published by Infinite Study. This book was released on with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the notions of CI-algebras, Smarandache CI-algebra, Q-Smarandache filters and Q-Smarandache ideals are introduced. Finally, we introduced the concepts of Smarandache BE-algebra, Smarandache dual BCK-algebra and Smarandache n-structure on CI-algebra.