Theory Of Commutative Fields
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Theory Of Commutative Fields
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Author : Masayoshi Nagata
language : en
Publisher: American Mathematical Soc.
Release Date :
Theory Of Commutative Fields written by Masayoshi Nagata 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 with Mathematics categories.
The theory of commutative fields is a fundamental area of mathematics, particularly in number theory, algebra, and algebraic geometry. However, few books provide sufficient treatment of this topic. The author aimed to provide an introduction to commutative fields that would be useful to those studying the topic for the first time as well as to those wishing a reference book. The book presents, with as few prerequisites as possible, all of the important and fundamental results on commutative fields. Each chapter ends with exercises, making the book suitable as a textbook for graduate courses or for independent study.
125
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Author : Masayoshi Nagata
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
125 written by Masayoshi Nagata 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 1993 with Mathematics categories.
The theory of commutative fields is a fundamental area of mathematics, particularly in number theory, algebra, and algebraic geometry. However, few books provide sufficient treatment of this topic. This book is a translation of the 1985 updated edition of Nagata's 1966 book; both editions originally appeared in Japanese. The author aimed to provide an introduction to commutative fields that would be useful to those studying the topic for the first time as well as to those wishing a reference book. The book presents, with as few prerequisites as possible, all of the important and fundamental results on commutative fields. Each chapter ends with exercises, making the book suitable as a textbook for graduate courses or for independent study.
Finite Commutative Rings And Their Applications
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Author : Gilberto Bini
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Finite Commutative Rings And Their Applications written by Gilberto Bini 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 Technology & Engineering categories.
Foreword by Dieter Jungnickel Finite Commutative Rings and their Applications answers a need for an introductory reference in finite commutative ring theory as applied to information and communication theory. This book will be of interest to both professional and academic researchers in the fields of communication and coding theory. The book is a concrete and self-contained introduction to finite commutative local rings, focusing in particular on Galois and Quasi-Galois rings. The reader is provided with an active and concrete approach to the study of the purely algebraic structure and properties of finite commutative rings (in particular, Galois rings) as well as to their applications to coding theory. Finite Commutative Rings and their Applications is the first to address both theoretical and practical aspects of finite ring theory. The authors provide a practical approach to finite rings through explanatory examples, thereby avoiding an abstract presentation of the subject. The section on Quasi-Galois rings presents new and unpublished results as well. The authors then introduce some applications of finite rings, in particular Galois rings, to coding theory, using a solid algebraic and geometric theoretical background.
Commutative Algebra
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Author : David Eisenbud
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Commutative Algebra written by David Eisenbud 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 2013-12-01 with Mathematics categories.
Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry. To help beginners, the essential ideals from algebraic geometry are treated from scratch. Appendices on homological algebra, multilinear algebra and several other useful topics help to make the book relatively self- contained. Novel results and presentations are scattered throughout the text.
Non Noetherian Commutative Ring Theory
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Author : S.T. Chapman
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-10-31
Non Noetherian Commutative Ring Theory written by S.T. Chapman 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 2000-10-31 with Mathematics categories.
This volume consists of twenty-one articles by many of the most prominent researchers in non-Noetherian commutative ring theory. The articles combine in various degrees surveys of past results, recent results that have never before seen print, open problems, and an extensive bibliography. One hundred open problems supplied by the authors have been collected in the volume's concluding chapter. The entire collection provides a comprehensive survey of the development of the field over the last ten years and points to future directions of research in the area. Audience: Researchers and graduate students; the volume is an appropriate source of material for several semester-long graduate-level seminars and courses.
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.
Commutative Ring Theory
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Author : Hideyuki Matsumura
language : en
Publisher: Cambridge University Press
Release Date : 1989-05-25
Commutative Ring Theory written by Hideyuki Matsumura 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 1989-05-25 with Mathematics categories.
This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.
Steps In Commutative Algebra
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Author : R. Y. Sharp
language : en
Publisher: Cambridge University Press
Release Date : 2000
Steps In Commutative Algebra written by R. Y. Sharp 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 2000 with Mathematics categories.
Introductory account of commutative algebra, aimed at students with a background in basic algebra.
Quantum Field Theory And Noncommutative Geometry
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Author : Ursula Carow-Watamura
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-02-21
Quantum Field Theory And Noncommutative Geometry written by Ursula Carow-Watamura 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 2005-02-21 with Mathematics categories.
This volume reflects the growing collaboration between mathematicians and theoretical physicists to treat the foundations of quantum field theory using the mathematical tools of q-deformed algebras and noncommutative differential geometry. A particular challenge is posed by gravity, which probably necessitates extension of these methods to geometries with minimum length and therefore quantization of space. This volume builds on the lectures and talks that have been given at a recent meeting on "Quantum Field Theory and Noncommutative Geometry." A considerable effort has been invested in making the contributions accessible to a wider community of readers - so this volume will not only benefit researchers in the field but also postgraduate students and scientists from related areas wishing to become better acquainted with this field.
Deformations Of Spacetime Symmetries
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Author : Michele Arzano
language : en
Publisher: Springer Nature
Release Date : 2021-06-14
Deformations Of Spacetime Symmetries written by Michele Arzano and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-14 with Science categories.
This monograph provides an introduction to deformations of Poincaré symmetries focusing on models with a Lie group momentum space and associated non-commutative space-times. The emphasis is put on the emergence of such structures from quantum gravity, their mathematical features described in terms of Hopf algebras and applications to particle kinematics and field theory. Part I of this work focuses on the link between gravity and deformed symmetries in the case of 2+1 and 3+1 space-time dimensions. Part II is devoted to the description of classical particles with group valued momenta, their phase spaces and kinematics. The last part of these notes provides an introduction to the basic features of classical and quantum field theory on κ-Minkowski space-time, the prototypical example of non-commutative space-time exhibiting deformed Poincaré symmetry. The text, being the first providing a detailed overview of these topics, is primarily intended for researchers and graduate students interested in non-commutative field theories and quantum gravity phenomenology.