If we take $F=\mathbb{C}$ and assume the Lie algebras involved are finite dimensional, is it true that if $\mathfrak{g}$ is nilpotent then it is the nilradical of some other Lie algebra $\mathfrak{h}$?

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    $\begingroup$ Every nilpotent algebra is its own nilradical. $\endgroup$ – Mariano Suárez-Álvarez Aug 22 '17 at 23:58
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    $\begingroup$ If you do not like that, then consider the direct sum of your nilpotent lie algebra and any semisimple one. $\endgroup$ – Mariano Suárez-Álvarez Aug 23 '17 at 0:00

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