习题 2, § 2

(a) 令$a, b$为戴德金域$A$的两个积分理想；表明存在一个积分理想 $c$，它与 $b$ 互质，并且 $ac$ 是主要的（应用命题 9 of § 1, no. 5）。

(b) Let $a, b$ be two integral ideals of $A$; show that there exists $x \neq 0$ in the field of fractions of $A$ such that $xa$ is an integral ideal of $A$ which is prime to $b$ (same method). 推论模$a/ab$与$A/b$同构的。