Algebraic Number Theory
《Algebraic Number Theory》 · 第 357 页 · Chapter VI，Section 1「Ideles and Idele Classes」
An adele of $K$ […] is a family $a=(a_{\mathfrak p})$ of elements $a_{\mathfrak p}\in K_{\mathfrak p}$ where $\mathfrak p$ runs through all primes of $K$, and $a_{\mathfrak p}$ is integral in $K_{\mathfrak p}$ for almost all $\mathfrak p$. The adeles form a ring, which is denoted by $\mathbb A_K=\prod_{\mathfrak p}'K_{\mathfrak p}$. […] This kind of product is called the “restricted product” of the $K_{\mathfrak p}$ with respect to the subrings $\mathfrak o_{\mathfrak p}\subseteq K_{\mathfrak p}$.