The Role Of Nonassociative Algebra In Projective Geometry
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The Role Of Nonassociative Algebra In Projective Geometry
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Author : John R. Faulkner
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-10-09
The Role Of Nonassociative Algebra In Projective Geometry written by John R. Faulkner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-09 with Mathematics categories.
There is a particular fascination when two apparently disjoint areas of mathematics turn out to have a meaningful connection to each other. The main goal of this book is to provide a largely self-contained, in-depth account of the linkage between nonassociative algebra and projective planes, with particular emphasis on octonion planes. There are several new results and many, if not most, of the proofs are new. The development should be accessible to most graduate students and should give them introductions to two areas which are often referenced but not often taught. On the geometric side, the book introduces coordinates in projective planes and relates coordinate properties to transitivity properties of certain automorphisms and to configuration conditions. It also classifies higher-dimensional geometries and determines their automorphisms. The exceptional octonion plane is studied in detail in a geometric context that allows nondivision coordinates. An axiomatic version of that context is also provided. Finally, some connections of nonassociative algebra to other geometries, including buildings, are outlined. On the algebraic side, basic properties of alternative algebras are derived, including the classification of alternative division rings. As tools for the study of the geometries, an axiomatic development of dimension, the basics of quadratic forms, a treatment of homogeneous maps and their polarizations, and a study of norm forms on hermitian matrices over composition algebras are included.
The Role Of Nonassociative Algebra In Projective Geometry
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Author : John R. Faulkner
language : en
Publisher:
Release Date : 2014
The Role Of Nonassociative Algebra In Projective Geometry written by John R. Faulkner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Geometry, Projective categories.
Non Associative Algebra And Its Applications
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Author : Lev Sabinin
language : en
Publisher: CRC Press
Release Date : 2006-01-13
Non Associative Algebra And Its Applications written by Lev Sabinin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-13 with Mathematics categories.
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. This book covers material such as Jordan superalgebras, nonassociative deformations, nonassociative generalization of Hopf algebras, the structure of free algebras, derivations of Lie algebras, and the identities of Albert algebra. It also includes applications of smooth quasigroups and loops to differential geometry and relativity.
Nonassociative Algebra And Its Applications
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Author : R Costa
language : en
Publisher: CRC Press
Release Date : 2019-05-20
Nonassociative Algebra And Its Applications written by R Costa and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-20 with Mathematics categories.
A collection of lectures presented at the Fourth International Conference on Nonassociative Algebra and its Applications, held in Sao Paulo, Brazil. Topics in algebra theory include alternative, Bernstein, Jordan, lie, and Malcev algebras and superalgebras. The volume presents applications to population genetics theory, physics, and more.
Introduction To Analytic And Probabilistic Number Theory
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Author : Gérald Tenenbaum
language : en
Publisher: American Mathematical Society
Release Date : 2024-06-26
Introduction To Analytic And Probabilistic Number Theory written by Gérald Tenenbaum and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-26 with Mathematics categories.
This book provides a self contained, thorough introduction to the analytic and probabilistic methods of number theory. The prerequisites being reduced to classical contents of undergraduate courses, it offers to students and young researchers a systematic and consistent account on the subject. It is also a convenient tool for professional mathematicians, who may use it for basic references concerning many fundamental topics. Deliberately placing the methods before the results, the book will be of use beyond the particular material addressed directly. Each chapter is complemented with bibliographic notes, useful for descriptions of alternative viewpoints, and detailed exercises, often leading to research problems. This third edition of a text that has become classical offers a renewed and considerably enhanced content, being expanded by more than 50 percent. Important new developments are included, along with original points of view on many essential branches of arithmetic and an accurate perspective on up-to-date bibliography. The author has made important contributions to number theory and his mastery of the material is reflected in the exposition, which is lucid, elegant, and accurate. —Mathematical Reviews
Lectures On Navier Stokes Equations
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Author : Tai-Peng Tsai
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-08-09
Lectures On Navier Stokes Equations written by Tai-Peng Tsai and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-09 with Mathematics categories.
This book is a graduate text on the incompressible Navier-Stokes system, which is of fundamental importance in mathematical fluid mechanics as well as in engineering applications. The goal is to give a rapid exposition on the existence, uniqueness, and regularity of its solutions, with a focus on the regularity problem. To fit into a one-year course for students who have already mastered the basics of PDE theory, many auxiliary results have been described with references but without proofs, and several topics were omitted. Most chapters end with a selection of problems for the reader. After an introduction and a careful study of weak, strong, and mild solutions, the reader is introduced to partial regularity. The coverage of boundary value problems, self-similar solutions, the uniform L3 class including the celebrated Escauriaza-Seregin-Šverák Theorem, and axisymmetric flows in later chapters are unique features of this book that are less explored in other texts. The book can serve as a textbook for a course, as a self-study source for people who already know some PDE theory and wish to learn more about Navier-Stokes equations, or as a reference for some of the important recent developments in the area.
Associative And Non Associative Algebras And Applications
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Author : Mercedes Siles Molina
language : en
Publisher: Springer Nature
Release Date : 2020-01-02
Associative And Non Associative Algebras And Applications written by Mercedes Siles Molina and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-02 with Mathematics categories.
This book gathers together selected contributions presented at the 3rd Moroccan Andalusian Meeting on Algebras and their Applications, held in Chefchaouen, Morocco, April 12-14, 2018, and which reflects the mathematical collaboration between south European and north African countries, mainly France, Spain, Morocco, Tunisia and Senegal. The book is divided in three parts and features contributions from the following fields: algebraic and analytic methods in associative and non-associative structures; homological and categorical methods in algebra; and history of mathematics. Covering topics such as rings and algebras, representation theory, number theory, operator algebras, category theory, group theory and information theory, it opens up new avenues of study for graduate students and young researchers. The findings presented also appeal to anyone interested in the fields of algebra and mathematical analysis.
Separable Algebras
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Author : Timothy J. Ford
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-09-26
Separable Algebras written by Timothy J. Ford and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-26 with Mathematics categories.
This book presents a comprehensive introduction to the theory of separable algebras over commutative rings. After a thorough introduction to the general theory, the fundamental roles played by separable algebras are explored. For example, Azumaya algebras, the henselization of local rings, and Galois theory are rigorously introduced and treated. Interwoven throughout these applications is the important notion of étale algebras. Essential connections are drawn between the theory of separable algebras and Morita theory, the theory of faithfully flat descent, cohomology, derivations, differentials, reflexive lattices, maximal orders, and class groups. The text is accessible to graduate students who have finished a first course in algebra, and it includes necessary foundational material, useful exercises, and many nontrivial examples.
The Theory Of Near Rings
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Author : Robert Lockhart
language : en
Publisher: Springer Nature
Release Date : 2021-11-14
The Theory Of Near Rings written by Robert Lockhart and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-14 with Mathematics categories.
This book offers an original account of the theory of near-rings, with a considerable amount of material which has not previously been available in book form, some of it completely new. The book begins with an introduction to the subject and goes on to consider the theory of near-fields, transformation near-rings and near-rings hosted by a group. The bulk of the chapter on near-fields has not previously been available in English. The transformation near-rings chapters considerably augment existing knowledge and the chapters on product hosting are essentially new. Other chapters contain original material on new classes of near-rings and non-abelian group cohomology. The Theory of Near-Rings will be of interest to researchers in the subject and, more broadly, ring and representation theorists. The presentation is elementary and self-contained, with the necessary background in group and ring theory available in standard references.
Lectures On Finite Fields
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Author : Xiang-dong Hou
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-06-07
Lectures On Finite Fields written by Xiang-dong Hou and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-07 with Mathematics categories.
The theory of finite fields encompasses algebra, combinatorics, and number theory and has furnished widespread applications in other areas of mathematics and computer science. This book is a collection of selected topics in the theory of finite fields and related areas. The topics include basic facts about finite fields, polynomials over finite fields, Gauss sums, algebraic number theory and cyclotomic fields, zeros of polynomials over finite fields, and classical groups over finite fields. The book is mostly self-contained, and the material covered is accessible to readers with the knowledge of graduate algebra; the only exception is a section on function fields. Each chapter is supplied with a set of exercises. The book can be adopted as a text for a second year graduate course or used as a reference by researchers.