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Cover: 9781441920959 | Field Theory | Steven Roman | Taschenbuch | Paperback | XII | Englisch
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Field Theory
Taschenbuch von Steven Roman
Sprache: Englisch

56,95 €*

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Lieferzeit 1-2 Wochen

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Beschreibung
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. 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
Zusammenfassung
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.
Inhaltsverzeichnis
Preliminaries.- Preliminaries.- Field Extensions.- Polynomials.- Field Extensions.- Embeddings and Separability.- Algebraic Independence.- Galois Theory.- Galois Theory I: An Historical Perspective.- Galois Theory II: The Theory.- Galois Theory III: The Galois Group of a Polynomial.- A Field Extension as a Vector Space.- Finite Fields I: Basic Properties.- Finite Fields II: Additional Properties.- The Roots of Unity.- Cyclic Extensions.- Solvable Extensions.- The Theory of Binomials.- Binomials.- Families of Binomials.
Details
Erscheinungsjahr: 2011
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 348
Reihe: Graduate Texts in Mathematics
Inhalt: xii
335 S.
18 s/w Illustr.
335 p. 18 illus.
ISBN-13: 9781441920959
ISBN-10: 1441920951
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Roman, Steven
Auflage: 2nd ed. 2006
Hersteller: Springer US
Springer New York
Graduate Texts in Mathematics
Maße: 235 x 155 x 19 mm
Von/Mit: Steven Roman
Erscheinungsdatum: 17.09.2011
Gewicht: 0,528 kg
preigu-id: 106971218
Zusammenfassung
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.
Inhaltsverzeichnis
Preliminaries.- Preliminaries.- Field Extensions.- Polynomials.- Field Extensions.- Embeddings and Separability.- Algebraic Independence.- Galois Theory.- Galois Theory I: An Historical Perspective.- Galois Theory II: The Theory.- Galois Theory III: The Galois Group of a Polynomial.- A Field Extension as a Vector Space.- Finite Fields I: Basic Properties.- Finite Fields II: Additional Properties.- The Roots of Unity.- Cyclic Extensions.- Solvable Extensions.- The Theory of Binomials.- Binomials.- Families of Binomials.
Details
Erscheinungsjahr: 2011
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 348
Reihe: Graduate Texts in Mathematics
Inhalt: xii
335 S.
18 s/w Illustr.
335 p. 18 illus.
ISBN-13: 9781441920959
ISBN-10: 1441920951
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Roman, Steven
Auflage: 2nd ed. 2006
Hersteller: Springer US
Springer New York
Graduate Texts in Mathematics
Maße: 235 x 155 x 19 mm
Von/Mit: Steven Roman
Erscheinungsdatum: 17.09.2011
Gewicht: 0,528 kg
preigu-id: 106971218
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