习题 7, § 8

令$K$为域，$v$为$v$的$K$、$A$环的估值，$m$为$v$的理想值。 假设$A$是Henselian；令$L$为次数$n$的$K$的有限扩张；令 $v'$ 为$L$ 扩展$v$ (习题 6 (e)) 的唯一估值，$A'$ 为环，$m'$ 为理想值。 Let $x$ be any element of $A'$; show that the degree over $A/m$ of the class $\bar{x}$ of $x$ in $A'/m'$ is a divisor of $n$ and that the order of the class of $v'(x)$ in $\Gamma_{v'}/\Gamma_v$ is a divisor of $n$ (consider the minimal polynomial of $x$ over $K$).