radical extension
A radical tower is a field extension which has a filtration
where for each , , there exists an element and a natural number such that and .
A radical extension is a field extension for which there exists a radical tower with . 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 is solvable by radicals if and only if its splitting field is a radical extension of .
Title | radical extension |
---|---|
Canonical name | RadicalExtension |
Date of creation | 2013-03-22 12:08:35 |
Last modified on | 2013-03-22 12:08:35 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 7 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 12F10 |
Synonym | radical tower |