---- Let $\mathfrak{g}$ be a [[Lie algebra]]. > [!definition] Definition. ([[radical of a Lie algebra]]) > The result [[sums preserve solvability of Lie algebra ideals]] means that $\mathfrak{g}$ has a unique maximal [[ideal of a Lie algebra|ideal]] obtained by summing all solvable ideals together. This ideal is called the **radical of $\mathfrak{g}$**, and denoted $\text{Rad}(\mathfrak{g})$. ^definition ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```