习题 10, § 1

Let $A$ be a Krull domain, $K$ its field of fractions, $L$ a field containing $K$ and $(B_i)$ a right directed family of Krull domains containing $A$ and contained in $L$ such that the field of fractions $L_\alpha$ of $B_i$ is a finite algebraic extension of $K$ and $B_i$ is the integral closure of $A$ in $L_\alpha$. 对于$A$和所有$a$的每个基本评估$v$，令$e_\alpha(v)$为$B_i$评估结果指标的和，其中扩展$v$。 证明，要使$B_i$的并成为克鲁尔域，对于$A$的每个基本评估$v$，$e_\alpha(v)$的集合有界是必要且充分的。