Lie Groups Beyond an Introduction
《Lie Groups Beyond an Introduction》 · 第 49、56 页 · Chapter I, Section 7「Cartan's Criterion for Semisimplicity」的底域约定及 Corollary 1.56 前的定义（省略中间无关文字）
In this section, $k$ denotes a subfield of $\mathbb C$, and $\mathfrak g$ denotes a finite-dimensional Lie algebra over $k$. […] We say that the Lie algebra $\mathfrak g$ is reductive if to each ideal $\mathfrak a$ in $\mathfrak g$ corresponds an ideal $\mathfrak b$ in $\mathfrak g$ with $\mathfrak g=\mathfrak a\oplus\mathfrak b$.