I believe these questions are trivial, but I still need some help.
Consider $\mathfrak{h}$ Lie subalgebra of the real $n-$dimensional Lie algebra $\mathfrak{g}$. Is there a non-trivial ideal $J$ of $\mathfrak{g}$ containing $\mathfrak{h}$?
Another question: If $\mathfrak{h}$ is nilpotent (still subalgebra, non-necessarily an ideal), may I consider $\mathfrak{h}$ contained in the nilrad of $\mathfrak{g}$?