Dedekind domains and their class groups are notions in commutative algebra that are essential in algebraic number theory. We formalized these structures and several fundamental properties, including number-theoretic finiteness results for class groups, in the Lean prover as part of the mathlib mathematical library. This paper describes the formalization process, noting the idioms we found useful in our development and mathlib’s decentralized collaboration processes involved in this project.

中文翻译：

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Dedekind 域和全局域类群的形式化

Dedekind 域及其类群是交换代数中的概念，在代数数论中是必不可少的。作为mathlib数学库的一部分，我们在精益证明器中形式化了这些结构和几个基本属性，包括类组的数论有限性结果。本文描述了形式化过程，指出了我们发现在我们的开发中有用的习语以及该项目中涉及的mathlib的分散式协作过程。