radical extension (original) (raw)

A radical tower is a field extension L/F which has a filtration

where for each i, 0≤i<n, there exists an element αi∈Li+1 and a natural number ni such that Li+1=Li⁢(αi) and αini∈Li.

A radical extension is a field extension K/F for which there exists a radical tower L/F with L⊃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.