Radical of a Lie algebra

In the mathematical field of Lie theory, the radical of a Lie algebra ${\displaystyle {\mathfrak {g}}}$ is the largest solvable ideal of ${\displaystyle {\mathfrak {g}}.}$

Let ${\displaystyle k}$ be a field and let ${\displaystyle {\mathfrak {g}}}$ be a finite-dimensional Lie algebra over ${\displaystyle k}$. There exists a unique maximal solvable ideal, called the radical, for the following reason.

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