Valued Fields (Springer Monographs in Mathematics) - Hardcover

Engler, Antonio J.; Prestel, Alexander

Hardcover

ISBN 10: 354024221X ISBN 13: 9783540242215

Verlag: Springer, 2005

Inhaltsangabe

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.

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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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2005
• Sprache: Englisch
• ISBN 10: 354024221X
• ISBN 13: 9783540242215
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 218
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland