Algebraic Number Theory
《Algebraic Number Theory》 · 第 120 页 · Chapter II，Section 3「Valuations」，定义段
Let $|\cdot|$ be a nonarchimedean valuation of the field $K$. Putting $v(x)=-\log|x|$ for $x\ne0$, and $v(0)=\infty$, we obtain a function $v:K\to\mathbb R\cup\{\infty\}$ with $v(x)=\infty\Longleftrightarrow x=0$, $v(xy)=v(x)+v(y)$, and $v(x+y)\geq\min\{v(x),v(y)\}$. A function $v$ on $K$ with these properties is called an exponential valuation of $K$.