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Theory Of Commutative Fields
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Book Synopsis Theory of Commutative Fields by : Masayoshi Nagata
Download or read book Theory of Commutative Fields written by Masayoshi Nagata and published by American Mathematical Soc.. This book was released on with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebraic Coding Theory Over Finite Commutative Rings by : Steven T. Dougherty
Download or read book Algebraic Coding Theory Over Finite Commutative Rings written by Steven T. Dougherty and published by Springer. This book was released on 2017-07-04 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to algebraic coding theory over finite Frobenius rings. It is the first to offer a comprehensive account on the subject. Coding theory has its origins in the engineering problem of effective electronic communication where the alphabet is generally the binary field. Since its inception, it has grown as a branch of mathematics, and has since been expanded to consider any finite field, and later also Frobenius rings, as its alphabet. This book presents a broad view of the subject as a branch of pure mathematics and relates major results to other fields, including combinatorics, number theory and ring theory. Suitable for graduate students, the book will be of interest to anyone working in the field of coding theory, as well as algebraists and number theorists looking to apply coding theory to their own work.
Author :Gabriel Daniel Villa Salvador Publisher :Springer Science & Business Media ISBN 13 :0817645152 Total Pages :658 pages Book Rating :4.8/5 (176 download)
Book Synopsis Topics in the Theory of Algebraic Function Fields by : Gabriel Daniel Villa Salvador
Download or read book Topics in the Theory of Algebraic Function Fields written by Gabriel Daniel Villa Salvador and published by Springer Science & Business Media. This book was released on 2007-10-10 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of numbers. The examination explains both the similarities and fundamental differences between function fields and number fields, including many exercises and examples to enhance understanding and motivate further study. The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra.
Book Synopsis Steps in Commutative Algebra by : R. Y. Sharp
Download or read book Steps in Commutative Algebra written by R. Y. Sharp and published by Cambridge University Press. This book was released on 2000 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory account of commutative algebra, aimed at students with a background in basic algebra.
Book Synopsis Topics in the Homological Theory of Modules Over Commutative Rings by : Melvin Hochster
Download or read book Topics in the Homological Theory of Modules Over Commutative Rings written by Melvin Hochster and published by American Mathematical Soc.. This book was released on 1975 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains expository lectures from the CBMS Regional Conference in Mathematics held at the University of Nebraska, June 1974. This book deals mainly with developments and still open questions in the homological theory of modules over commutative (usually, Noetherian) rings.
Download or read book Field Theory written by Masayoshi Nagata and published by . This book was released on 1977 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction To Commutative Algebra by : Michael F. Atiyah
Download or read book Introduction To Commutative Algebra written by Michael F. Atiyah and published by CRC Press. This book was released on 2018-03-09 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 2018. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.
Book Synopsis Commutative Ring Theory by : Hideyuki Matsumura
Download or read book Commutative Ring Theory written by Hideyuki Matsumura and published by Cambridge University Press. This book was released on 1989-05-25 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.
Book Synopsis Commutative Algebra by : David Eisenbud
Download or read book Commutative Algebra written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.
Book Synopsis An Introduction to Commutative Algebra and Number Theory by : Sukumar Das Adhikari
Download or read book An Introduction to Commutative Algebra and Number Theory written by Sukumar Das Adhikari and published by CRC Press. This book was released on 2001-11 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an elementary introduction to algebra and number theory. The text begins by a review of groups, rings, and fields. The algebra portion addresses polynomial rings, UFD, PID, and Euclidean domains, field extensions, modules, and Dedckind domains. The number theory portion reviews elementary congruence, quadratic reciprocity, algebraic number fields, and a glimpse into the various aspects of that subject. This book could be used as a one semester course in graduate mathematics.
Download or read book Field Theory written by Steven Roman and published by Springer. This book was released on 2013-12-20 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for graduate courses or for independent study, this book presents the basic theory of fields. The first part begins with a discussion of polynomials over a ring, the division algorithm, irreducibility, field extensions, and embeddings. The second part is devoted to Galois theory. The third part of the book treats the theory of binomials. The book concludes with a chapter on families of binomials - the Kummer theory.
Book Synopsis Advanced Classical Field Theory by : G. Giachetta
Download or read book Advanced Classical Field Theory written by G. Giachetta and published by World Scientific. This book was released on 2009 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contemporary quantum field theory is mainly developed as quantization of classical fields. Therefore, classical field theory and its BRST extension is the necessary step towards quantum field theory. This book aims to provide a complete mathematical foundation of Lagrangian classical field theory and its BRST extension for the purpose of quantization. Based on the standard geometric formulation of theory of nonlinear differential operators, Lagrangian field theory is treated in a very general setting. Reducible degenerate Lagrangian theories of even and odd fields on an arbitrary smooth manifold are considered. The second Noether theorems generalized to these theories and formulated in the homology terms provide the strict mathematical formulation of BRST extended classical field theory. The most physically relevant field theories OCo gauge theory on principal bundles, gravitation theory on natural bundles, theory of spinor fields and topological field theory OCo are presented in a complete way. This book is designed for theoreticians and mathematical physicists specializing in field theory. The authors have tried throughout to provide the necessary mathematical background, thus making the exposition self-contained.
Author :Supriya Kar Publisher :World Scientific Publishing Company Incorporated ISBN 13 :9789812380524 Total Pages :250 pages Book Rating :4.3/5 (85 download)
Book Synopsis Non-commutative Geometry by : Supriya Kar
Download or read book Non-commutative Geometry written by Supriya Kar and published by World Scientific Publishing Company Incorporated. This book was released on 2018-01-31 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic, comprehensive and up-to-date account of the recent developments in non-commutative geometry, at a pedagogical level. It does not go into the details of rigorous (advanced level) mathematical formulation of non-commutative geometry; rather, it restricts itself to the domain of strings and quantum fields.Since non-commutative geometry has recently aroused renewed interest in open string theory, the author motivates the text from the viewpoint of a string theory. He begins with an introduction to the subject, explaining what one means by non-commutative geometry and why it is relevant to study such geometry, and discussing its possible origin in a string theory.The book comprises nine chapters. Chapter 1 gives a sound mathematical ntroduction to non-commutative spacetime coordinates in classical and quantum physics. In Chapter 2, non-commutativity in a string theory is discussed at a pedagogic level. Chapter 3 deals with an aribitrary D-brane dynamics and Chapter 4 describes the non-commutative gauge theories on a D-brane. In Chapters 5-9, non-commutative quantum field theory (NCQFT) is addressed. In particular, Chapter 5 deals with the real scalar NCQFT, Chapter 6 with that of complex scalar field, Chapter 7 describes spontaneous symmetry breaking in scalar NCQFT, Chapter 8 deals with the U(1) Gauge theory and Chapter 9 with SU(n) Gauge theories.Students will find this book useful as a bridge between string and field theories. In addition, it will prove invaluable for interdisciplinary areas of study.
Book Synopsis Multiplicative Ideal Theory in Commutative Algebra by : James W. Brewer
Download or read book Multiplicative Ideal Theory in Commutative Algebra written by James W. Brewer and published by Springer Science & Business Media. This book was released on 2006-12-15 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, a tribute to the work of Robert Gilmer, consists of twenty-four articles authored by his most prominent students and followers. These articles combine surveys of past work by Gilmer and others, recent results which have never before seen print, open problems, and extensive bibliographies. The entire collection provides an in-depth overview of the topics of research in a significant and large area of commutative algebra.
Book Synopsis Basic Commutative Algebra by : Balwant Singh
Download or read book Basic Commutative Algebra written by Balwant Singh and published by World Scientific. This book was released on 2011 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook, set for a one or two semester course in commutative algebra, provides an introduction to commutative algebra at the postgraduate and research levels. The main prerequisites are familiarity with groups, rings and fields. Proofs are self-contained. The book will be useful to beginners and experienced researchers alike. The material is so arranged that the beginner can learn through self-study or by attending a course. For the experienced researcher, the book may serve to present new perspectives on some well-known results, or as a reference.
Book Synopsis Fields and Rings by : Irving Kaplansky
Download or read book Fields and Rings written by Irving Kaplansky and published by University of Chicago Press. This book was released on 1972 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book combines in one volume Irving Kaplansky's lecture notes on the theory of fields, ring theory, and homological dimensions of rings and modules. "In all three parts of this book the author lives up to his reputation as a first-rate mathematical stylist. Throughout the work the clarity and precision of the presentation is not only a source of constant pleasure but will enable the neophyte to master the material here presented with dispatch and ease."—A. Rosenberg, Mathematical Reviews
Book Synopsis Finite Commutative Rings and Their Applications by : Gilberto Bini
Download or read book Finite Commutative Rings and Their Applications written by Gilberto Bini and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
