Let $\g$ be a Lie algebra. Since the sum of any two solvable ideals of $\g$ is in turn solvable, there is a unique maximal solvable ideal of any Lie algebra. This ideal is called the radical of $\g$ . Note that $\g/\mathrm{rad}\,\g$ has no solvable ideals, and is thus semi-simple. Thus, every Lie algebra is an extension of a semi-simple algebra by a solvable one.