splitting field
Let $f\in F[x]$ be a polynomial^{} over a field $F$. A splitting field^{} for $f$ is a field extension $K$ of $F$ such that

1.
$f$ splits (factors into a product of linear factors) in $K[x]$,

2.
$K$ is the smallest field with this property (any subextension field of $K$ which satisfies the first property is equal to $K$).
Theorem: Any polynomial over any field has a splitting field, and any two such splitting fields are isomorphic. A splitting field is always a normal extension^{} of the ground field.
Title  splitting field 

Canonical name  SplittingField 
Date of creation  20130322 12:08:01 
Last modified on  20130322 12:08:01 
Owner  djao (24) 
Last modified by  djao (24) 
Numerical id  7 
Author  djao (24) 
Entry type  Definition 
Classification  msc 12F05 
Related topic  NormalExtension 