Algebraic Number Theory
《Algebraic Number Theory》 · 第 123 页 · Chapter II，Section 4「Valuations of Arbitrary Rank」
A Krull valuation of a field $K$ is a map $v:K\to\Gamma\cup\{\infty\}$ into an ordered abelian group $\Gamma$, augmented by $\infty$, such that $v(xy)=v(x)+v(y)$, $v(x+y)\geq\min\{v(x),v(y)\}$, and $v(x)=\infty$ if and only if $x=0$.