Quasigroups and Loops
Author: Orin Chein
Publisher:
Published: 1990
Total Pages: 596
ISBN-13:
DOWNLOAD EBOOKPosts
Quasigroups and Loops
Author: Hala O. Pflugfelder
Publisher:
Published: 1990
Total Pages: 172
ISBN-13:
DOWNLOAD EBOOKSmooth Quasigroups and Loops
Author: L. Sabinin
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 263
ISBN-13: 9401144915
DOWNLOAD EBOOKDuring 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.
A Study of New Concepts in Smarandache Quasigroups and Loops
Author: Jaiyeola Temitope Gbolahan
Publisher: Infinite Study
Published: 2009
Total Pages: 139
ISBN-13: 1599730839
DOWNLOAD EBOOKThis 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.
An Introduction to Quasigroups and Their Representations
Author: Jonathan D. H. Smith
Publisher: CRC Press
Published: 2006-11-15
Total Pages: 353
ISBN-13: 1420010638
DOWNLOAD EBOOKCollecting 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,
Loops in Group Theory and Lie Theory
Author: Péter T. Nagy
Publisher: Walter de Gruyter
Published: 2002
Total Pages: 384
ISBN-13: 9783110170108
DOWNLOAD EBOOKIn 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.
Elements of Quasigroup Theory and Applications
Author: Victor Shcherbacov
Publisher: CRC Press
Published: 2017-05-12
Total Pages: 423
ISBN-13: 1351646362
DOWNLOAD EBOOKThis 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.
Elements of Quasigroup Theory and Applications
Author: Victor Shcherbacov
Publisher: CRC Press
Published: 2017-05-12
Total Pages: 599
ISBN-13: 1498721567
DOWNLOAD EBOOKUnderstanding 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.
Post-Modern Algebra
Author: Jonathan D. H. Smith
Publisher: John Wiley & Sons
Published: 2011-09-30
Total Pages: 386
ISBN-13: 1118030834
DOWNLOAD EBOOKAdvanced 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.
Mathematical Combinatorics, Vol. 1/2008
Author: Linfan Mao
Publisher: Infinite Study
Published:
Total Pages: 109
ISBN-13: 1599730502
DOWNLOAD EBOOKPapers 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.
