Lie Groups Beyond an Introduction
《Lie Groups Beyond an Introduction》 · 印刷第 81 页 Chapter I，Section 11「Covering Groups」的拓扑空间约定及第 88 页 Proposition 1.97 完整陈述、随后命名句和证明中的单位元说明；唯一性是在固定覆盖单位元 $\widetilde1$ 后理解
Proposition. Let $V$ be a finite dimensional vector space over $F$, $x \in \operatorname{End} V$. (a) There exist unique $x_s, x_n \in \operatorname{End} V$ satisfying the conditions: $x = x_s + x_n$, $x_s$ is semisimple, $x_n$ is nilpotent, $x_s$ and $x_n$ commute. […] The decomposition $x = x_s + x_n$ is called the (additive) Jordan-Chevalley decomposition of $x$, or just the Jordan decomposition; $x_s, x_n$ are called (respectively) the semisimple part and the nilpotent part of $x$.