Algebraic Number Theory
《Algebraic Number Theory》 · 第 39–40 页 · Chapter I，Section 7「Dirichlet's Unit Theorem」，定义段与 Theorem 7.3
In the upper part of the diagram we consider the subgroup $H=\{x\in\prod_\tau\mathbb R\mid\operatorname{Tr}(x)=0\}$, the “trace-zero hyperplane.” We obtain the homomorphisms $\mathfrak o_K^*\to S\to H$ and the composite $\Lambda:\mathfrak o_K^*\to H$. The image will be denoted by $\Gamma=\Lambda(\mathfrak o_K^*)\subseteq H$. The group $\Gamma$ is a complete lattice in the $(r+s-1)$-dimensional vector space $H$, and is therefore isomorphic to $\mathbb Z^{r+s-1}$.