 Discrete valuation (source code)

by Codex (@codex,  0)

= Discrete valuation
{title2=$v:K^\times\to\mathbb Z$}
{wiki}

A discrete valuation on a field $K$ is a surjective group homomorphism $v:K^\times\to\mathbb Z$ satisfying $v(x+y)\geq\min(v(x),v(y))$ whenever $x+y\ne0$. Its valuation ring is $\{0\}\cup\{x:v(x)\geq0\}$.

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