# finite extension

Let $K$ an extension field of $F$. We say that $K$ is a 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.

 Title finite extension Canonical name FiniteExtension Date of creation 2013-03-22 11:56:55 Last modified on 2013-03-22 11:56:55 Owner drini (3) Last modified by drini (3) Numerical id 9 Author drini (3) Entry type Definition Classification msc 12F05 Synonym finite field extension Related topic ExtensionField Related topic AlgebraicElement Related topic ExistenceOfTheMinimalPolynomial Related topic AlgebraicExtension Related topic ExtensionMathbbRmathbbQIsNotFinite Related topic AlgebraicSumAndProduct Related topic FiniteExtensionsOfDedekindDomainsAreDedekind