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Groupoids And Smarandache Groupoids
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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.
Book Synopsis SMARANDACHE SOFT GROUPOIDS by : Mumtaz Ali
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.
Author :W. B. Vasantha Kandasamy, Florentin Smarandache Publisher :Infinite Study ISBN 13 :159973222X Total Pages :151 pages Book Rating :4.5/5 (997 download)
Book Synopsis Subset Groupoids by : W. B. Vasantha Kandasamy, Florentin Smarandache
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:
Book Synopsis Groupoids of Type I and II Using [0, n) by : W. B. Vasantha Kandasamy
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.
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).
Book Synopsis Interval Groupoids by : W. B. Vasantha Kandasamy
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.
Book Synopsis Subset Interval Groupoids by : W. B. Vasantha Kandasamy
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:
Book Synopsis A Study of New Concepts in Smarandache Quasigroups and Loops by : Jaiyeola Temitope Gbolahan
Download or read book A Study of New Concepts in Smarandache Quasigroups and Loops written by Jaiyeola Temitope Gbolahan and published by Infinite Study. This book was released on 2009 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a compilation of results on some new Smarandache concepts in Smarandache;groupoids, quasigroups and loops, and it pin points the inter-relationships and connections between andamong the various Smarandache concepts and notions that have been developed. This monograph isstructured into six chapters. The first chapter is an introduction to the theory quasigroups and loops withmuch attention paid to those quasigroup and loop concepts whose Smarandache versions are to bestudied in the other chapters. In chapter two, the holomorphic structures of Smarandache loops ofBol-Moufang type and Smarandache loops of non-Bol-Moufang type are studied. In the third chapter,the notion of parastrophy is introduced into Smarandache quasigroups and studied. Chapter four studiesthe universality of some Smarandache loops of Bol-Moufang type. In chapter five, the notion ofSmarandache isotopism is introduced and studied in Smarandache quasigroups and loops. In chaptersix, by introducing Smarandache special mappings in Smarandache groupoids, the SmarandacheBryant-Schneider group of a Smarandache loop is developed.
Book Synopsis An Introduction to Groups, Groupoids and Their Representations by : Alberto Ibort
Download or read book An Introduction to Groups, Groupoids and Their Representations written by Alberto Ibort and published by CRC Press. This book was released on 2019-10-28 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to the theory of groupoids and their representations encompassing the standard theory of groups. Using a categorical language, developed from simple examples, the theory of finite groupoids is shown to knit neatly with that of groups and their structure as well as that of their representations is described. The book comprises numerous examples and applications, including well-known games and puzzles, databases and physics applications. Key concepts have been presented using only basic notions so that it can be used both by students and researchers interested in the subject. Category theory is the natural language that is being used to develop the theory of groupoids. However, categorical presentations of mathematical subjects tend to become highly abstract very fast and out of reach of many potential users. To avoid this, foundations of the theory, starting with simple examples, have been developed and used to study the structure of finite groups and groupoids. The appropriate language and notions from category theory have been developed for students of mathematics and theoretical physics. The book presents the theory on the same level as the ordinary and elementary theories of finite groups and their representations, and provides a unified picture of the same. The structure of the algebra of finite groupoids is analysed, along with the classical theory of characters of their representations. Unnecessary complications in the formal presentation of the subject are avoided. The book offers an introduction to the language of category theory in the concrete setting of finite sets. It also shows how this perspective provides a common ground for various problems and applications, ranging from combinatorics, the topology of graphs, structure of databases and quantum physics.
Book Synopsis Groupoids in Analysis, Geometry, and Physics by : Arlan Ramsay
Download or read book Groupoids in Analysis, Geometry, and Physics written by Arlan Ramsay and published by American Mathematical Soc.. This book was released on 2001 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Groupoids often occur when there is symmetry of a nature not expressible in terms of groups. Other uses of groupoids can involve something of a dynamical nature. Indeed, some of the main examples come from group actions. It should also be noted that in many situations where groupoids have been used, the main emphasis has not been on symmetry or dynamics issues. While the implicit symmetry and dynamics are relevant, the groupoid records mostly the structure of the space of leaves and the holonomy. More generally, the use of groupoids is very much related to various notions of orbit equivalance. This book presents the proceedings from the Joint Summer Research Conference on ``Groupoids in Analysis, Geometry, and Physics'' held in Boulder, CO. The book begins with an introduction to ways in which groupoids allow a more comprehensive view of symmetry than is seen via groups. Topics range from foliations, pseudo-differential operators, $KK$-theory, amenability, Fell bundles, and index theory to quantization of Poisson manifolds. Readers will find examples of important tools for working with groupoids. This book is geared to students and researchers. It is intended to improve their understanding of groupoids and to encourage them to look further while learning about the tools used.
Book Synopsis Generalized Fibonacci sequences in groupoids by : Hee Sik Kim
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.
Author :Madad Khan, Florentin Smarandache, Saima Anis Publisher :Infinite Study ISBN 13 :1599733471 Total Pages :210 pages Book Rating :4.5/5 (997 download)
Book Synopsis Theory of Abel Grassmann's Groupoids by : Madad Khan, Florentin Smarandache, Saima Anis
Download or read book Theory of Abel Grassmann's Groupoids written by Madad Khan, Florentin Smarandache, Saima Anis and published by Infinite Study. This book was released on 2015-04-01 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: We extend now for the first time the AG-groupoid to the Neutrosophic AG-groupoid. A neutrosophic AG-groupoid is a neutrosophic algebraic structure that lies between a neutrosophic groupoid and a neutrosophic commutative semigroup.
Book Synopsis Bilagebraic Structures and Smarandache Bialgebraic Structures by : W. B. Vasantha Kandasamy
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.
Book Synopsis Some Implicativities for Groupoids and BCK-Algebras by : In Ho Hwang
Download or read book Some Implicativities for Groupoids and BCK-Algebras written by In Ho Hwang and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we generalize the notion of an implicativity discussed in BCK-algebras, and apply it to some groupoids and BCK-algebras. We obtain some relations among those axioms in the theory of groupoids.
Book Synopsis Groupoids, Inverse Semigroups, and their Operator Algebras by : Alan Paterson
Download or read book Groupoids, Inverse Semigroups, and their Operator Algebras written by Alan Paterson and published by Springer Science & Business Media. This book was released on 1999 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, it has become increasingly clear that there are important connections relating three concepts -- groupoids, inverse semigroups, and operator algebras. There has been a great deal of progress in this area over the last two decades, and this book gives a careful, up-to-date and reasonably extensive account of the subject matter. After an introductory first chapter, the second chapter presents a self-contained account of inverse semigroups, locally compact and r-discrete groupoids, and Lie groupoids. The section on Lie groupoids in chapter 2 contains a detailed discussion of groupoids particularly important in noncommutative geometry, including the holonomy groupoids of a foliated manifold and the tangent groupoid of a manifold. The representation theories of locally compact and r-discrete groupoids are developed in the third chapter, and it is shown that the C*-algebras of r-discrete groupoids are the covariance C*-algebras for inverse semigroup actions on locally compact Hausdorff spaces. A final chapter associates a universal r-discrete groupoid with any inverse semigroup. Six subsequent appendices treat topics related to those covered in the text. The book should appeal to a wide variety of professional mathematicians and graduate students in fields such as operator algebras, analysis on groupoids, semigroup theory, and noncommutative geometry. It will also be of interest to mathematicians interested in tilings and theoretical physicists whose focus is modeling quasicrystals with tilings. An effort has been made to make the book lucid and 'user friendly"; thus it should be accessible to any reader with a basic background in measure theory and functional analysis.
Book Synopsis Scientia Magna Vol. 6, No. 1, 2010 by : Zhang Wenpeng
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.
Book Synopsis Scientia Magna, Vol. 1, No. 2, 2005 by : Zhang Wenpeng
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.
