Introduction to p-Adic Numbers and Valuation Theory

The field of p-adic numbers, which can be obtained from the field of rational numbers by a completion process with respect to a special kind of mapping, or valuation, similar in many respects to the ordinary absolute value mapping has a great number of interesting properties. However, beyond this, it turns out that such fields are of particular interest and importance in algebraic number theory and algebraic geometry. This is equally true of the general notion of a valuation together with some of its related concepts. The book is meant to serve as an introduction to valuation theory.