normal extension

A field extension $K/F$ is normal if every irreducible polynomial $f\in F[x]$ which has at least one root in $K$ splits (factors into a product of linear factors) in $K[x]$.

An extension $K/F$ of finite degree is normal if and only if there exists a polynomial $p\in F[x]$ such that $K$ is the splitting field for $p$ over $F$.

Title	normal extension
Canonical name	NormalExtension
Date of creation	2013-03-22 12:08:15
Last modified on	2013-03-22 12:08:15
Owner	djao (24)
Last modified by	djao (24)
Numerical id	10
Author	djao (24)
Entry type	Definition
Classification	msc 12F10
Synonym	normal
Related topic	SplittingField