Number Fields
《Number Fields》 · 第 91 页 · Chapter 5「The Ideal Class Group and the Unit Group」开篇
Recall that the ideal class group of a number ring $R$ consists of equivalence classes of nonzero ideals under the relation $I\sim J$ iff $\alpha I=\beta J$ for some nonzero $\alpha,\beta\in R$; the group operation is multiplication defined in the obvious way.