A radical tower is a field extension $L/F$ which has a filtration
 $F=L_{0}\subset L_{1}\subset\cdots\subset L_{n}=L$
where for each $i$, $0\leq i, there exists an element $\alpha_{i}\in L_{i+1}$ and a natural number $n_{i}$ such that $L_{i+1}=L_{i}(\alpha_{i})$ and $\alpha_{i}^{n_{i}}\in L_{i}$.
A radical extension is a field extension $K/F$ for which there exists a radical tower $L/F$ with $L\supset K$. The notion of radical extension coincides with the informal concept of solving for the roots of a polynomial by radicals, in the sense that a polynomial over $K$ is solvable by radicals if and only if its splitting field is a radical extension of $F$.