augmentation ideal for universal enveloping algebras

Question

Let $L$ be a restricted Lie algebra with the restricted enveloping algebra $u(L)$ over a field $F$. Let $ω(L)$ denote the augmentation ideal of $u(L)$ which is the kernel of the augmentation map $\varepsilon : u(L) \mapsto F$ induced by $x\mapsto 0$. My question is as follows: Why the augmentation ideal is generated by $L$? May you please give an example?