finite extension FiniteExtension 2001-11-08 01:28:04 2003-05-21 22:19:47 Definition Galois Theory Field \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} Let $K$ an extension field of $F$. We say that $K$ is a \emph{finite extension} if $[K:F]$ is finite. That is, $K$ is a finite dimensional space over $F$. An important result on finite extensions establishes that any finite extension is also an algebraic extension.