Algebraic Number Theory
《Algebraic Number Theory》 · 第 358 页 · Chapter VI，Section 1「Ideles and Idele Classes」
The inclusions $K\subseteq K_{\mathfrak p}$ allow us to define the diagonal embedding $K^*\longrightarrow I_K$, which associates to $a\in K^*$ the idele whose $\mathfrak p$-th component is the element $a$ in $K_{\mathfrak p}$. We thus view $K^*$ as a subgroup of $I_K$ and we call the elements of $K^*$ in $I_K$ principal ideles.