论文标题
主要理想的激进分子和Dedekind领域的班级组
Radicals of principal ideals and the class group of a Dedekind domain
论文作者
论文摘要
对于Dedekind域$ D $，令$ \ Mathcal {p}（d）$是$ d $的理想集，这些理想是主要理想的。我们表明，如果$ d，d'US是Dedekind域，并且在$ \ Mathcal {p}（d）$和$ \ Mathcal {p}（d'）$之间存在订单同构，那么$ d $和$ d'$的类等级是相同的。
For a Dedekind domain $D$, let $\mathcal{P}(D)$ be the set of ideals of $D$ that are radical of a principal ideal. We show that, if $D,D'$ are Dedekind domains and there is an order isomorphism between $\mathcal{P}(D)$ and $\mathcal{P}(D')$, then the rank of the class groups of $D$ and $D'$ is the same.
