ABSTRACT

We give a definition of a class of Dedekind domains which includes the rings of integers of global fields and give a proof that all rings in this class have finite ideal class group. We also prove that this class coincides with the class of rings of integers of global fields.

中文翻译：

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全球场类组有限性的一致证明

摘要

我们给出一类Dedekind域的定义，其中包括全局字段整数的环，并证明该类中的所有环都具有有限的理想类组。我们还证明了该类别与全局字段整数环的类别一致。