Valuation Theory and Its Applications, Volume I

Valuation theory arose in the early part of the twentieth century in connection with number theory and has many important applications to geometry and analysis: the classical application to the study of algebraic curves and to Dedekind and Prüfer domains; the close connection to the famous resolution of the singularities problem; the study of the absolute Galois group of a field; the connection between ordering, valuations, and quadratic forms over a formally real field; the application to real algebraic geometry; the study of noncommutative rings; etc. The special feature of this book is its focus on current applications of valuation theory to this broad range of topics. Also included is a paper on the history of valuation theory.

The book is suitable for graduate students and research mathematicians working in algebra, algebraic geometry, number theory, and mathematical logic.