Skew Fields
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Units In Skew Fields
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Author : Ernst Kleinert
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Units In Skew Fields written by Ernst Kleinert and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is devoted to a study of the unit groups of orders in skew fields, finite dimensional and central over the rational field; it thereby belongs to the field of noncommutative arithmetic. Its purpose is a synopsis of results and methods, including full proofs of the most important results. It is addressed to researchers in number theory and arithmetic groups.
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. K. Draxl
language : en
Publisher: Cambridge University Press
Release Date : 1983-02-17
Skew Fields written by P. K. Draxl 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 1983-02-17 with Mathematics categories.
The book is written in three parts. Part I consists of preparatory work on algebras, needed in Parts II and III. Part II consists of a modern description of the theory of Brauer groups over fields (from as elementary a point of view as possible). Part III covers some new developments in the theory which, until now, have not been available except in journals.
The Classical Fields
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Author : H. Salzmann
language : en
Publisher: Cambridge University Press
Release Date : 2007-08-23
The Classical Fields written by H. Salzmann 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 2007-08-23 with Mathematics categories.
The real, rational, complex and p-adic numbers are discussed in detail in this comprehensive work.
A Guide To Groups Rings And Fields
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Author : Fernando Q. Gouvêa
language : en
Publisher: MAA
Release Date : 2012
A Guide To Groups Rings And Fields written by Fernando Q. Gouvêa and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
Insightful overview of many kinds of algebraic structures that are ubiquitous in mathematics. For researchers at graduate level and beyond.
The Global Approach To Quantum Field Theory
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Author : Bryce Seligman DeWitt
language : en
Publisher: Oxford University Press, USA
Release Date : 2003
The Global Approach To Quantum Field Theory written by Bryce Seligman DeWitt and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Science categories.
This new volume takes a complete look at how classical field theory, quantum mechanics and quantum field theory are interrelated. It takes a global approach and discusses the importance of quantization by relating it to different theories such as tree amplitude and conservation laws. There arespecial chapters devoted to Euclideanization and renormalization, space and time inversion and the closed-time-path formalism.
Methods In Ring Theory
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Author : Freddy Van Oystaeyen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Methods In Ring Theory written by Freddy Van Oystaeyen 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 2012-12-06 with Mathematics categories.
Proceedings of the NATO Advanced Study Institute, Antwerp, Belgium, August 2-12, 1983
Representation Of Rings Over Skew Fields
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Author : Aidan Harry Schofield
language : en
Publisher: Cambridge University Press
Release Date : 1985
Representation Of Rings Over Skew Fields written by Aidan Harry Schofield 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 1985 with Mathematics categories.
A study of representations of rings over skew fields.
Abstract Algebra
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Author : Joseph H. Silverman
language : en
Publisher: American Mathematical Society
Release Date : 2022-03-07
Abstract Algebra written by Joseph H. Silverman 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 2022-03-07 with Mathematics categories.
This abstract algebra textbook takes an integrated approach that highlights the similarities of fundamental algebraic structures among a number of topics. The book begins by introducing groups, rings, vector spaces, and fields, emphasizing examples, definitions, homomorphisms, and proofs. The goal is to explain how all of the constructions fit into an axiomatic framework and to emphasize the importance of studying those maps that preserve the underlying algebraic structure. This fast-paced introduction is followed by chapters in which each of the four main topics is revisited and deeper results are proven. The second half of the book contains material of a more advanced nature. It includes a thorough development of Galois theory, a chapter on modules, and short surveys of additional algebraic topics designed to whet the reader's appetite for further study. This book is intended for a first introduction to abstract algebra and requires only a course in linear algebra as a prerequisite. The more advanced material could be used in an introductory graduate-level course.