Buch, Englisch, 208 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 494 g
Buch, Englisch, 208 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 494 g
Reihe: Springer Monographs in Mathematics
ISBN: 978-3-540-24221-5
Verlag: Springer Berlin Heidelberg
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
- Mathematik | Informatik Mathematik Algebra Zahlentheorie
- Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
- Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
Weitere Infos & Material
Absolute Values.- Valuations.- Extension of Valuations.- Henselian Fields.- Structure Theory.- Applications of Valuation Theory.
