习题 6, § 1

Let $A$ be a commutative ring and $B$ a commutative $A$-algebra; suppose that the minimal prime ideals of B are finite in number; let $p_i$ ($1 \leq i \leq n$) be these ideals (note that this hypothesis holds if B is Noetherian). 为了使元素$x \in B$在A上积分，$B/p_i$中的每个典范像$x_i$在A上积分是充分必要的。（如果这个条件成立，首先证明$x$是由B的零根$\mathfrak{N} = \bigcap_i p_i$生成的B的子代数积分，并且利用元素或 $\mathfrak{N}$ 幂零的事实。）