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Cover: 9783642063459 | Valued Fields | Alexander Prestel (u. a.) | Taschenbuch | x | Englisch
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Valued Fields
Taschenbuch von Alexander Prestel (u. a.)
Sprache: Englisch

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Beschreibung
Absolute values and their completions -like the p-adic number fields- play an important role in number theory. Krull's generalization of absolute values to valuations made applications in other branches of mathematics, such as algebraic geometry, possible. In valuation theory, the notion of a completion has to be replaced by that of the so-called Henselization.

In this book, the theory of valuations as well as of Henselizations is developed. The presentation is based on the knowledge acquired in a standard graduate course in algebra. The last chapter presents three applications of the general theory -for instance to Artin's Conjecture on the p-adic number fields- that could not be obtained by the use of absolute values alone.
Absolute values and their completions -like the p-adic number fields- play an important role in number theory. Krull's generalization of absolute values to valuations made applications in other branches of mathematics, such as algebraic geometry, possible. In valuation theory, the notion of a completion has to be replaced by that of the so-called Henselization.

In this book, the theory of valuations as well as of Henselizations is developed. The presentation is based on the knowledge acquired in a standard graduate course in algebra. The last chapter presents three applications of the general theory -for instance to Artin's Conjecture on the p-adic number fields- that could not be obtained by the use of absolute values alone.
Zusammenfassung
Absolute values and their completions - such as the p-adic number fields - play an important role in number theory. Krull's generalization of absolute values to valuations made applications in other branches of mathematics, such as algebraic geometry, possible. In valuation theory, the notion of a completion has to be replaced by that of "Henselization". This book develops the theory of valuations as well as of Henselizations, based on the knowledge acquired in a standard graduate course in algebra.
Inhaltsverzeichnis
Absolute Values.- Valuations.- Extension of Valuations.- Henselian Fields.- Structure Theory.- Applications of Valuation Theory.
Details
Erscheinungsjahr: 2010
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: x
208 S.
ISBN-13: 9783642063459
ISBN-10: 3642063454
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Prestel, Alexander
Engler, Antonio J.
Hersteller: Springer Berlin
Springer Berlin Heidelberg
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 12 mm
Von/Mit: Alexander Prestel (u. a.)
Erscheinungsdatum: 21.10.2010
Gewicht: 0,335 kg
Artikel-ID: 107023046
Zusammenfassung
Absolute values and their completions - such as the p-adic number fields - play an important role in number theory. Krull's generalization of absolute values to valuations made applications in other branches of mathematics, such as algebraic geometry, possible. In valuation theory, the notion of a completion has to be replaced by that of "Henselization". This book develops the theory of valuations as well as of Henselizations, based on the knowledge acquired in a standard graduate course in algebra.
Inhaltsverzeichnis
Absolute Values.- Valuations.- Extension of Valuations.- Henselian Fields.- Structure Theory.- Applications of Valuation Theory.
Details
Erscheinungsjahr: 2010
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: x
208 S.
ISBN-13: 9783642063459
ISBN-10: 3642063454
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Prestel, Alexander
Engler, Antonio J.
Hersteller: Springer Berlin
Springer Berlin Heidelberg
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 12 mm
Von/Mit: Alexander Prestel (u. a.)
Erscheinungsdatum: 21.10.2010
Gewicht: 0,335 kg
Artikel-ID: 107023046
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