terminology - Translation of "le nilradicalisé de g"

I apologize for asking something that might well be found in a mathematical dictionary, but the similarity of the French word to an English one is frustrating my attempts to Google the answer (and the library is shut at time of typing). I suspect the answer should be obvious to those who, unlike me, know some basic Lie group/Lie algebra terminology.

Some context: I am reading an old paper of Dixmier from 1969, which has the following construction/definition. Let $mathfrak g$ be a Lie algebra (characteristic zero, finite-dimensional), let $mathfrak n$ be its largest nilpotent ideal -- the nilradical -- and put ${mathfrak h}=[{mathfrak g},{mathfrak g}]+{mathfrak n}$. Dixmier calls ${mathfrak h}$ "le nilradicalisé de ${mathfrak g}$".

Literal translation would surely be "the nilradicalised", but that sounds more like a mopey university indie band than a mathematical object. So what is the usual name for this object in English?