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＜E-Book＞
Valued Fields / by Antonio J. Engler, Alexander Prestel
(Springer Monographs in Mathematics. ISSN:21969922)

Edition	1st ed. 2005.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	2005
Language	English
Size	X, 208 p : online resource
Authors	*Engler, Antonio J author Prestel, Alexander author SpringerLink (Online service)
Subjects	LCSH:Algebra LCSH:Number theory LCSH:Algebraic geometry LCSH:Mathematical logic FREE:Algebra FREE:Number Theory FREE:Algebraic Geometry FREE:Mathematical Logic and Foundations
Notes	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 HTTP:URL=https://doi.org/10.1007/3-540-30035-X

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