Valued fields / Antonio J. Engler, Alexander Prestel.
Material type:
TextSeries: Springer monographs in mathematicsPublication details: Berlin : Springer, 2005.Description: 190 pISBN: - 354024221x
- QA247 .E54 2005
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| QA241 .R67 1992 Elementary number theory and its applications / | QA246 .C74 2005 Prime Numbers: A Computational Perspective/ | QA246 E78 2012 Little big books : illustrations for children's picture books / | QA247 .E54 2005 Valued fields / | QA247 .M24 2014 Lecture notes on algebraic structure of lattice-ordered rings / | QA247 .S4613 1979 Local fields / | QA247 .S4613 1979 Local fields / |
Bibliographic references pp199-200.
Absolute Values.- Valuations.- Extension of Valuations.- Henselian Fields.- Structure Theory.- Applications of Valuation Theory.- Ultraproducts of Valued Fields.- Classification of V-topologies.
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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