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Sinopsis
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.
This new edition has been completely rewritten in order to improve the pedagogy and to make the text more accessible to graduate students. The exercises have also been improved and a new chapter on ordered fields has been included.
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De la contraportada
This book presents the basic theory of fields, starting more or less from the beginning. It is suitable for a graduate course in field theory, or independent study. The reader is expected to have taken an undergraduate course in abstract algebra, not so much for the material it contains but in order to gain a certain level of mathematical maturity.
For this new edition, the author has rewritten the text based on his experiences teaching from the first edition. There are new exercises, a new chapter on Galois theory from an historical perspective, and additional topics sprinkled throughout the text, including a proof of the Fundamental Theorem of Algebra, a discussion of casus irreducibilis, Berlekamp's algorithm for factoring polynomials over Zp and natural and accessory irrationalities.
From the reviews of the first edition:
The book is written in a clear and explanatory style...the book is recommended for a graduate course in field theory as well as for independent study.
- T. Albu, Mathematical Reviews
...[the author] does an excellent job of stressing the key ideas. This book should not only work well as a textbook for a beginning graduate course in field theory, but also for a student who wishes to take a field theory course as independent study.
- J.N.Mordeson, Zentralblatt
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Field Theory (Graduate Texts in Mathematics, 158)
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Field Theory (Graduate Texts in Mathematics, 158)
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Field Theory (Paperback)
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ISBN 10: 1441920951
ISBN 13: 9781441920959
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Paperback. Condición: new. Paperback. 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. This new edition has been completely rewritten in order to improve the pedagogy and to make the text more accessible to graduate students. The exercises have also been improved and a new chapter on ordered fields has been included.About the first edition:" .the author has gotten across many important ideas and results. This book should not only work well as a textbook for a beginning graduate course in field theory, but also for a student who wishes to take a field theory course as independent study."-J.N. Mordeson, Zentralblatt"The book is written in a clear and explanatory style. It contains over 235 exercises which provide a challenge to the reader. The book is recommended for a graduate course in field theory as well as for independent study."- T. Albu, MathSciNet Intended for graduate courses or for independent study, this book presents the basic theory of fields. This book should not only work well as a textbook for a beginning graduate course in field theory, but also for a student who wishes to take a field theory course as independent study."-J.N. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Nº de ref. del artículo: 9781441920959
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Field Theory
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Springer New York, Springer US Sep 2011, 2011
ISBN 10: 1441920951
ISBN 13: 9781441920959
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Taschenbuch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. This new edition has been completely rewritten in order to improve the pedagogy and to make the text more accessible to graduate students. The exercises have also been improved and a new chapter on ordered fields has been included.About the first edition:' .the author has gotten across many important ideas and results. This book should not only work well as a textbook for a beginning graduate course in field theory, but also for a student who wishes to take a field theory course as independent study.'-J.N. Mordeson, Zentralblatt'The book is written in a clear and explanatory style. It contains over 235 exercises which provide a challenge to the reader. The book is recommended for a graduate course in field theory as well as for independent study.'- T. Albu, MathSciNet 348 pp. Englisch. Nº de ref. del artículo: 9781441920959
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