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 $i$ $0 \leq i < n$ 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 $F$