Lectures on Formally Real Fields (Paperback)

A. Prestel

ISBN 10: 3540138854 / ISBN 13: 9783540138853

Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin, 1984

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Paperback. 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 aquired 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. Absolute values and their completions - like the p-adic number fields- play an important role in number theory. 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. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Codice articolo 9783540138853

Dati bibliografici

• Titolo: Lectures on Formally Real Fields (Paperback)
• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin
• Data di pubblicazione: 1984
• Lingua: Inglese
• ISBN 10: 3540138854
• ISBN 13: 9783540138853
• Rilegatura: Paperback
• Condizione: new

Descrizione articolo

Riassunto

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 aquired 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.

Contenuti

Orderings and semiorderings of fields.- Quadratic forms over formally real fields.- Real algebraic closures.- Some notions from model theory.- The transfer-principle for real closed fields.- The space of orderings and semiorderings.- Real places.- Real henselian fields.- SAP-fields.- Quadratic forms over formally real fields.