习题 6, § 3

An integral domain $A$ is called integrally Noetherian if it is Noetherian and if, for every finite sequence $(t_i)_{1 \leq i \leq n}$ of elements of an extension field of the field of fractions of $A$, the integral closure of $A[t_1, \ldots, t_n]$ is a finitely generated $A[t_1, \ldots, t_n]$-module. 每个在域上有限生成的积分代数都是一个积分诺特域（no. 2，定理 2）。

(a) 积分诺特域上的每个有限生成的积分代数都是积分诺特域。未减至 0 的整数诺特域的分数的每个环都是整数诺特域。

(b) Let $A$ be an integrally Noetherian domain $(t_i)_{1 \leq i \leq n}$ a finite sequence of elements of an extension field of the field of fractions $K$ of $A$ and $B$ a subring of $K(t_1, \ldots, t_n)$ containing $A$ and integral over $A$. 那么$B$是一个有限生成的$A$-模块。 （注，$B$的分数的域是$K$的有限代数扩张，使用代数、章V, § 5, no. 7。）