Download or read book Quasigroups and Loops written by Orin Chein and published by . This book was released on 1990 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quasigroups and Loops written by Hala O. Pflugfelder and published by . This book was released on 1990 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Smooth Quasigroups and Loops written by L. Sabinin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last twenty-five years quite remarkable relations between nonas sociative algebra and differential geometry have been discovered in our work. Such exotic structures of algebra as quasigroups and loops were obtained from purely geometric structures such as affinely connected spaces. The notion ofodule was introduced as a fundamental algebraic invariant of differential geometry. For any space with an affine connection loopuscular, odular and geoodular structures (partial smooth algebras of a special kind) were introduced and studied. As it happened, the natural geoodular structure of an affinely connected space al lows us to reconstruct this space in a unique way. Moreover, any smooth ab stractly given geoodular structure generates in a unique manner an affinely con nected space with the natural geoodular structure isomorphic to the initial one. The above said means that any affinely connected (in particular, Riemannian) space can be treated as a purely algebraic structure equipped with smoothness. Numerous habitual geometric properties may be expressed in the language of geoodular structures by means of algebraic identities, etc.. Our treatment has led us to the purely algebraic concept of affinely connected (in particular, Riemannian) spaces; for example, one can consider a discrete, or, even, finite space with affine connection (in the form ofgeoodular structure) which can be used in the old problem of discrete space-time in relativity, essential for the quantum space-time theory.
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.
Download or read book An Introduction to Quasigroups and Their Representations written by Jonathan D. H. Smith and published by CRC Press. This book was released on 2006-11-15 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collecting results scattered throughout the literature into one source, An Introduction to Quasigroups and Their Representations shows how representation theories for groups are capable of extending to general quasigroups and illustrates the added depth and richness that result from this extension. To fully understand representation theory,
Download or read book Loops in Group Theory and Lie Theory written by Péter T. Nagy and published by Walter de Gruyter. This book was released on 2002 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the theory of binary systems is considered as a part of group theory and, in particular, within the framework of Lie groups. The novelty is the consequent treatment of topological and differentiable loops as topological and differentiable sections in Lie groups. The interplay of methods and tools from group theory, differential geometry and topology, symmetric spaces, topological geometry, and the theory of foliations is what gives a special flavour to the results presented in this book. It is the first monograph devoted to the study of global loops. So far books on differentiable loops deal with local loops only. This theory can only be used partially for the theory of global loops since non-associative local structures have, in general, no global forms. The text is addressed to researchers in non-associative algebra and foundations of geometry. It should prove enlightening to a broad range of readers, including mathematicians working in group theory, the theory of Lie groups, in differential and topological geometry, and in algebraic groups. The authors have produced a text that is suitable not only for a graduate course, but also for selfstudy in the subjectby interested graduate students. Moreover, the material presented can be used for lectures and seminars in algebra, topological algebra and geometry.
Download or read book Elements of Quasigroup Theory and Applications written by Victor Shcherbacov and published by CRC Press. This book was released on 2017-05-12 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to quasigroup theory along with new structural results on some of the quasigroup classes. Many results are presented with some of them from mathematicians of the former USSR. These included results have not been published before in the western mathematical literature. In addition, many of the achievements obtained with regard to applications of quasigroups in coding theory and cryptology are described.
Download or read book Elements of Quasigroup Theory and Applications written by Victor Shcherbacov and published by CRC Press. This book was released on 2017-05-12 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding Interaction is a book that explores the interaction between people and technology, in the broader context of the relations between the human made and the natural environments. It is not just about digital technologies – our computers, smart phones, the Internet – but all our technologies such as mechanical, electrical and electronic. Our ancestors started creating mechanical tools and shaping their environments millions of years ago, developing cultures and languages, which in turn influenced our evolution. Volume 1 of Understanding Interaction looks into this deep history – starting from the tool creating period (the longest and most influential on our physical and mental capacities), to the settlement period (agriculture, domestication, villages and cities, written language), the industrial period (science, engineering, reformation and renaissance), and finally the communication period (mass media, digital technologies, global networks). Volume 2 looks into humans in interaction – our physiology, anatomy, neurology, psychology, how we experience and influence the world, and how we (think we) think. From this transdisciplinary understanding, design approaches and frameworks are presented, to potentially guide future developments and innovations. The aim of the book is to be guide and inspiration for designers, artists, engineers, psychologists, media producers, social scientists etc., and as such be useful for both novices and more experienced practitioners.
Download or read book Latin Squares and Their Applications written by A. Donald Keedwell and published by Elsevier. This book was released on 2015-07-28 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: Latin Squares and Their Applications, Second edition offers a long-awaited update and reissue of this seminal account of the subject. The revision retains foundational, original material from the frequently-cited 1974 volume but is completely updated throughout. As with the earlier version, the author hopes to take the reader 'from the beginnings of the subject to the frontiers of research'. By omitting a few topics which are no longer of current interest, the book expands upon active and emerging areas. Also, the present state of knowledge regarding the 73 then-unsolved problems given at the end of the first edition is discussed and commented upon. In addition, a number of new unsolved problems are proposed. Using an engaging narrative style, this book provides thorough coverage of most parts of the subject, one of the oldest of all discrete mathematical structures and still one of the most relevant. However, in consequence of the huge expansion of the subject in the past 40 years, some topics have had to be omitted in order to keep the book of a reasonable length. Latin squares, or sets of mutually orthogonal latin squares (MOLS), encode the incidence structure of finite geometries; they prescribe the order in which to apply the different treatments in designing an experiment in order to permit effective statistical analysis of the results; they produce optimal density error-correcting codes; they encapsulate the structure of finite groups and of more general algebraic objects known as quasigroups. As regards more recreational aspects of the subject, latin squares provide the most effective and efficient designs for many kinds of games tournaments and they are the templates for Sudoku puzzles. Also, they provide a number of ways of constructing magic squares, both simple magic squares and also ones with additional properties. - Retains the organization and updated foundational material from the original edition - Explores current and emerging research topics - Includes the original 73 'Unsolved Problems' with the current state of knowledge regarding them, as well as new Unsolved Problems for further study
Download or read book Post Modern Algebra written by Jonathan D. H. Smith and published by John Wiley & Sons. This book was released on 2011-09-30 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced algebra in the service of contemporary mathematicalresearch-- a unique introduction. This volume takes an altogether new approach to advanced algebra.Its intriguing title, inspired by the term postmodernism, denotes adeparture from van der Waerden's Modern Algebra--a book that hasdominated the field for nearly seventy years. Post-Modern Algebraoffers a truly up-to-date alternative to the standard approach,explaining topics from an applications-based perspective ratherthan by abstract principles alone. The book broadens the field ofstudy to include algebraic structures and methods used in currentand emerging mathematical research, and describes the powerful yetsubtle techniques of universal algebra and category theory.Classical algebraic areas of groups, rings, fields, and vectorspaces are bolstered by such topics as ordered sets, monoids,monoid actions, quasigroups, loops, lattices, Boolean algebras,categories, and Heyting algebras. The text features: * A clear and concise treatment at an introductory level, tested inuniversity courses. * A wealth of exercises illustrating concepts and their practicalapplication. * Effective techniques for solving research problems in the realworld. * Flexibility of presentation, making it easy to tailor material tospecific needs. * Help with elementary proofs and algebraic notations for studentsof varying abilities. Post-Modern Algebra is an excellent primary or supplementary textfor graduate-level algebra courses. It is also an extremely usefulresource for professionals and researchers in many areas who musttackle abstract, linear, or universal algebra in the course oftheir work.
Download or read book Mathematical Combinatorics Vol 1 2008 written by Linfan Mao and published by Infinite Study. This book was released on with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers on flexibility of Embeddings of a Halin Graph on the Projective Plane, curvature Equations on Combinatorial Manifolds with Applications to Theoretical Physics, a Pair of Smarandachely Isotopic Quasigroups and Loops of the Same Variety, and similar topics. Contributors: Arun S. Muktibodh, Han Ren, Yun Bai, Yuhua Fu, Anjie Fushenglin Cao, Guangxuan Wang, and others.
Download or read book On the Classification of Bol Moufang Type of Some Varieties of Quasi Neutrosophic Triplet Loop Fenyves BCI Algebras written by Tèmítópé Gbóláhàn Jaíyéolá and published by Infinite Study. This book was released on with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, Bol-Moufang types of a particular quasi neutrosophic triplet loop (BCI-algebra), chritened Fenyves BCI-algebras are introduced and studied. 60 Fenyves BCI-algebras are introduced and classified. Amongst these 60 classes of algebras, 46 are found to be associative and 14 are found to be non-associative. The 46 associative algebras are shown to be Boolean groups.
Download or read book A Gyrovector Space Approach to Hyperbolic Geometry written by Abraham Ungar and published by Morgan & Claypool Publishers. This book was released on 2009-03-08 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mere mention of hyperbolic geometry is enough to strike fear in the heart of the undergraduate mathematics and physics student. Some regard themselves as excluded from the profound insights of hyperbolic geometry so that this enormous portion of human achievement is a closed door to them. The mission of this book is to open that door by making the hyperbolic geometry of Bolyai and Lobachevsky, as well as the special relativity theory of Einstein that it regulates, accessible to a wider audience in terms of novel analogies that the modern and unknown share with the classical and familiar. These novel analogies that this book captures stem from Thomas gyration, which is the mathematical abstraction of the relativistic effect known as Thomas precession. Remarkably, the mere introduction of Thomas gyration turns Euclidean geometry into hyperbolic geometry, and reveals mystique analogies that the two geometries share. Accordingly, Thomas gyration gives rise to the prefix "gyro" that is extensively used in the gyrolanguage of this book, giving rise to terms like gyrocommutative and gyroassociative binary operations in gyrogroups, and gyrovectors in gyrovector spaces. Of particular importance is the introduction of gyrovectors into hyperbolic geometry, where they are equivalence classes that add according to the gyroparallelogram law in full analogy with vectors, which are equivalence classes that add according to the parallelogram law. A gyroparallelogram, in turn, is a gyroquadrilateral the two gyrodiagonals of which intersect at their gyromidpoints in full analogy with a parallelogram, which is a quadrilateral the two diagonals of which intersect at their midpoints. Table of Contents: Gyrogroups / Gyrocommutative Gyrogroups / Gyrovector Spaces / Gyrotrigonometry
Download or read book Non Associative Algebra and Its Applications written by Lev Sabinin and published by CRC Press. This book was released on 2006-01-13 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions derived from presentations at an international conference, Non-Associative Algebra and Its Applications explores a wide range of topics focusing on Lie algebras, nonassociative rings and algebras, quasigroups, loops, and related systems as well as applications of nonassociative algebra to geometry, physics, and natural sciences.
Download or read book Mathematical Combinatorics Vol 3 2008 written by Linfan Mao and published by Infinite Study. This book was released on with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers on Extending Homomorphism Theorem to Multi-Systems, A Double Cryptography Using the Smarandache Keedwell Cross Inverse Quasigroup, the Time-like Curves of Constant Breadth in Minkowski 3-Space, Actions of Multi-groups on Finite Sets, and other topics. Contributors: Linfan Mao, Zhongfu Zhang, Enqiang Zhu, Baogen Xu, S. Arumugam, I. Sahul Hamid, A.P. Santhakumaran, S.V. Ullas Chandran, M.M.M. Jaradat, M.F. Janem, A.J. Alawneh, and others.
Download or read book Foundations of Translation Planes written by Mauro Biliotti and published by CRC Press. This book was released on 2001-07-13 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exploration of the construction and analysis of translation planes to spreads, partial spreads, co-ordinate structures, automorphisms, autotopisms, and collineation groups. It emphasizes the manipulation of incidence structures by various co-ordinate systems, including quasisets, spreads and matrix spreadsets. The volume showcases methods of str
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).
