normal extension NormalExtension 2002-01-05 02:10:03 2006-11-30 19:55:45 Definition \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} A field extension $K/F$ is \emph{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 $F$.