Introduction to Lie Algebras and Representation Theory
《Introduction to Lie Algebras and Representation Theory》 · 第 6 页 · Section 2.1「Ideals」
It is natural to analyze the structure of a Lie algebra by looking at its ideals. If $L$ has no ideals except itself and $0$, and if moreover $[LL]\ne0$, we call $L$ simple. The condition $[LL]\ne0$ (i.e., $L$ nonabelian) is imposed in order to avoid giving undue prominence to the one dimensional algebra.