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 -for instance to Artin's Conjecture on the p-adic number fields- that could not be obtained by the use of absolute values alone.
From the reviews: "The book starts with the basic notion of absolute values followed by a comprehensive introduction to the theory of Krull valuations of arbitrary rank leading eventually to some deep results of recent research. ... A useful feature of the book are its two appendices dealing with classification of V-topologies and ultraproducts of valued fields. The concise style and choice of material makes this book a wonderful reading. It is a unique, original exposition full of valuable insights." (Sudesh Kaur Khanduja, Zentralblatt MATH, Vol. 1128 (6), 2008)
Innehållsförteckning
Absolute Values.- Valuations.- Extension of Valuations.- Henselian Fields.- Structure Theory.- Applications of Valuation Theory.
Heinz-Dieter Ebbinghaus, Hans Hermes, Friedrich Hirzebruch, Max Koecher, Klaus Mainzer, Jürgen Neukirch, Alexander Prestel, Reinhold Remmert, Klaus Lamotke
Heinz-Dieter Ebbinghaus, Hans Hermes, Friedrich Hirzebruch, Max Koecher, Klaus Mainzer, Jürgen Neukirch, Alexander Prestel, Reinhold Remmert, John H. Ewing