Valued Fields
By: Engler, Antonio J [author.].
Contributor(s): Prestel, Alexander [author.] | SpringerLink (Online service).
Material type:
BookSeries: Springer Monographs in Mathematics: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005.Description: X, 208 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540300359.Subject(s): Mathematics | Algebra | Algebraic geometry | Mathematical logic | Number theory | Mathematics | Algebra | Number Theory | Algebraic Geometry | Mathematical Logic and FoundationsDDC classification: 512 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
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E books
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PK Kelkar Library, IIT Kanpur | Available | EBK6461 |
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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