## You are here

Homeradical extension

## Primary tabs

# radical extension

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 $F$.

Synonym:

radical tower

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

12F10*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff