Skew Field Constructions

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Skew Field Constructions

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Author : P. M. Cohn
language : en
Publisher: CUP Archive
Release Date : 1977-04-28

Skew Field Constructions written by P. M. Cohn and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-04-28 with Mathematics categories.

"These notes describe methods of constructing skew fields, in particular the coproduct coconstruction discovered by the author, and trace out some of the consequences using the powerful coproduct theorems of G.M. Bergman, which are proved here."- publisher

Skew Fields

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Author : Paul Moritz Cohn
language : en
Publisher: Cambridge University Press
Release Date : 1995-07-28

Skew Fields written by Paul Moritz Cohn and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-07-28 with Mathematics categories.

Non-commutative fields (also called skew fields or division rings) have not been studied as thoroughly as their commutative counterparts and most accounts have hitherto been confined to division algebras, that is skew fields finite-dimensional over their centre. Based on the author's LMS lecture note volume Skew Field Constructions, the present work offers a comprehensive account of skew fields. The axiomatic foundation and a precise description of the embedding problem are followed by an account of algebraic and topological construction methods, in particular, the author's general embedding theory is presented with full proofs, leading to the construction of skew fields. The powerful coproduct theorems of G. M. Bergman are proved here as well as the properties of the matrix reduction functor, a useful but little-known construction providing a source of examples and counter-examples. The construction and basic properties of existentially closed skew fields are given, leading to an example of a model class with an infinite forcing companion which is not axiomatizable. The treatment of equations over skew fields has been simplified and extended by the use of matrix methods, and the beginnings of non-commutative algebraic geometry are presented, with a precise account of the problems that need to be overcome for a satisfactory theory. A separate chapter describes valuations and orderings on skew fields, with a construction applicable to free fields. Numerous exercises test the reader's understanding, presenting further aspects and open problems in concise form, and notes and comments at the ends of chapters provide historical background.

Skew Fields

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Author : P M Cohn, Frs
language : en
Publisher:
Release Date : 2014-05-14

Skew Fields written by P M Cohn, Frs and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with MATHEMATICS categories.

This work offers a comprehensive account of skew fields and related mathematics.

Algebra And Its Applications

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Author : D. V. Huynh
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Algebra And Its Applications written by D. V. Huynh 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 2006 with Mathematics categories.

This volume consists of contributions by speakers at a Conference on Algebra and its Applications that took place in Athens, Ohio, in March of 2005. It provides a snapshot of the diversity of themes and applications that interest algebraists today. The papers in this volume include some of the latest results in the theory of modules, noncommutative rings, representation theory, matrix theory, linear algebra over noncommutative rings, cryptography, error-correcting codes over finite rings, and projective-geometry codes, as well as expository articles that will provide algebraists and other mathematicians, including graduate students, with an accessible introduction to areas outside their own expertise. The book will serve both the specialist looking for the latest result and the novice seeking an accessible reference for some of the ideas and results presented here.

Algebraic Structures And Applications

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Author : Sergei Silvestrov
language : en
Publisher: Springer Nature
Release Date : 2020-06-18

Algebraic Structures And Applications written by Sergei Silvestrov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-18 with Mathematics categories.

This book explores the latest advances in algebraic structures and applications, and focuses on mathematical concepts, methods, structures, problems, algorithms and computational methods important in the natural sciences, engineering and modern technologies. In particular, it features mathematical methods and models of non-commutative and non-associative algebras, hom-algebra structures, generalizations of differential calculus, quantum deformations of algebras, Lie algebras and their generalizations, semi-groups and groups, constructive algebra, matrix analysis and its interplay with topology, knot theory, dynamical systems, functional analysis, stochastic processes, perturbation analysis of Markov chains, and applications in network analysis, financial mathematics and engineering mathematics. The book addresses both theory and applications, which are illustrated with a wealth of ideas, proofs and examples to help readers understand the material and develop new mathematical methods and concepts of their own. The high-quality chapters share a wealth of new methods and results, review cutting-edge research and discuss open problems and directions for future research. Taken together, they offer a source of inspiration for a broad range of researchers and research students whose work involves algebraic structures and their applications, probability theory and mathematical statistics, applied mathematics, engineering mathematics and related areas.

Elliptic Structures On 3 Manifolds

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Author : Charles Benedict Thomas
language : en
Publisher: Cambridge University Press
Release Date : 1986-08-21

Elliptic Structures On 3 Manifolds written by Charles Benedict Thomas and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-08-21 with Mathematics categories.

This volume will give a systematic exposition of known results for free actions by finite groups on S. The text begins with preliminary material on Seifert manifolds and group classification. This is followed by sections dealing with related topics including free bZe/2 and bZe/3 actions on lens/prism manifolds, the reduction theorem and tangential structure.

Permutation Groups And Combinatorial Structures

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Author : Norman Biggs
language : en
Publisher: Cambridge University Press
Release Date : 1979-08-16

Permutation Groups And Combinatorial Structures written by Norman Biggs and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-08-16 with Mathematics categories.

The subject of this book is the action of permutation groups on sets associated with combinatorial structures. Each chapter deals with a particular structure: groups, geometries, designs, graphs and maps respectively. A unifying theme for the first four chapters is the construction of finite simple groups. In the fifth chapter, a theory of maps on orientable surfaces is developed within a combinatorial framework. This simplifies and extends the existing literature in the field. The book is designed both as a course text and as a reference book for advanced undergraduate and graduate students. A feature is the set of carefully constructed projects, intended to give the reader a deeper understanding of the subject.

Ring Theory Antwerp 1980

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Author : F. van Oystaeyen
language : en
Publisher: Springer
Release Date : 2006-11-15

Ring Theory Antwerp 1980 written by F. van Oystaeyen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Finite Dimensional Division Algebras Over Fields

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Author : Nathan Jacobson
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-09

Finite Dimensional Division Algebras Over Fields written by Nathan Jacobson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-09 with Mathematics categories.

Here, the eminent algebraist, Nathan Jacobsen, concentrates on those algebras that have an involution. Although they appear in many contexts, these algebras first arose in the study of the so-called "multiplication algebras of Riemann matrices". Of particular interest are the Jordan algebras determined by such algebras, and thus their structure is discussed in detail. Two important concepts also dealt with are the universal enveloping algebras and the reduced norm. However, the largest part of the book is the fifth chapter, which focuses on involutorial simple algebras of finite dimension over a field.

Encyclopaedia Of Mathematics

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Author : M. Hazewinkel
language : en
Publisher: Springer
Release Date : 2013-11-11

Encyclopaedia Of Mathematics written by M. Hazewinkel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.