We explore the connection between atomicity in Prüfer domains and their corresponding class groups. We observe that a class group of infinite order is necessary for non-Noetherian almost Dedekind and Prüfer domains of finite character to be atomic. We construct a non-Noetherian almost Dedekind domain and exhibit a generating set for the ideal class semigroup.

中文翻译：

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Prüfer域中的理想类（半）基团和原子性

我们探索了Prüfer域中原子性及其对应的类组之间的联系。我们观察到，对于具有有限特征的非Noetherian几乎Dedekind和Prüfer域是原子的，无限级的类组是必需的。我们构造了一个非Noetherian几乎Dedekind域，并展示了理想类半群的生成集。