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Valued Fields

  • Kartonierter Einband
  • 216 Seiten
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Absolute values and their completions -like the p-adic number fields- play an important role in number theory. Krull's generalizat... Weiterlesen
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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.



Includes new chapter on valuation rings, definable in the language of fields only

Contains in addition a Galois theoretic characterization of the field of p-adic numbers

Written by experts



Inhalt
Absolute Values.- Valuations.- Extension of Valuations.- Henselian Fields.- Structure Theory.- Applications of Valuation Theory.

Produktinformationen

Titel: Valued Fields
Autor:
EAN: 9783642063459
ISBN: 3642063454
Format: Kartonierter Einband
Herausgeber: Springer Berlin Heidelberg
Anzahl Seiten: 216
Gewicht: 335g
Größe: H235mm x B155mm x T11mm
Jahr: 2010
Auflage: 2005

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