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