Number Fields
《Number Fields》 · 第 39 页 · Chapter 3「Prime Decomposition in Number Rings」开篇 Definition
A Dedekind domain is an integral domain $R$ such that (1) Every ideal is finitely generated; (2) Every nonzero prime ideal is a maximal ideal; (3) $R$ is integrally closed in its field of fractions $K=\{\alpha/\beta:\alpha,\beta\in R,\beta\ne0\}$.