Radical extension
= Radical extension
In the strict tower convention, a radical extension is a field obtained through finitely many adjunctions $a_i^{n_i}\in K_{i-1}$, $K_i=K_{i-1}(a_i)$. Some texts instead use the term for any subfield of such a tower. This distinction matters: <solvability by radicals> implies containment in a tower, and need not give a radical tower entirely inside the original field.