Tag Info

A valuation is a function on a field that provides a notion of size or multiplicity for elements of a field. More specifically, a valuation is surjective function from the unit group of a field to an ordered abelian group. An example of a valuation is the $p$-adic valuation on $\Bbb{Q}$. A field with a valuation on it is known as a valued field. Valuations are very useful tools that are often used in the study of algebraic geometry and algebraic number theory. Some topics in valuation theory include valuation extensions, such as Chevalley's extension theorem, and Henselian fields.