E Book

Valued Fields

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Absolute Values -- Valuations -- Extension of Valuations -- Henselian Fields -- Structure Theory -- Applications of Valuation Theory.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 -as to Artin's Conjecture on the p-adic number fields- that could not be obtained by the use of absolute values only.

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Ketersediaan

Informasi Detail

Judul Seri

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No. Panggil

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Penerbit

Berlin, Heidelberg : Springer., 2005

Deskripsi Fisik

X, 208 p.online resource.

Bahasa

English

ISBN/ISSN

9783540300359

Klasifikasi

512

Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

1st ed. 2005.

Subjek

Mathematical logic.
Mathematical Logic and Foundations.
Number theory.
Algebra.
Algebraic geometry.

Info Detail Spesifik

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Pernyataan Tanggungjawab

Antonio J. Engler, Alexander Prestel.

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