Introduction to Lie Algebras and Representation Theory
《Introduction to Lie Algebras and Representation Theory》 · 第 15 页 · Chapter II 的底域约定及 Section 4.1「Lie's Theorem」的 Theorem（省略无关过渡文字）
Virtually all of the remaining theory to be developed in this book will require the assumption that $F$ have characteristic $0$. (Some of the exercises will indicate how counterexamples arise in prime characteristic.) Moreover, in order to have available the eigenvalues of $\operatorname{ad}x$ for arbitrary $x$ (not just for $\operatorname{ad}x$ nilpotent), we shall assume that $F$ is algebraically closed, except where otherwise specified. […] Theorem. Let $L$ be a solvable subalgebra of $\mathfrak{gl}(V)$, $V$ finite dimensional. If $V\ne0$, then $V$ contains a common eigenvector for all the endomorphisms in $L$.