finite extension

Let K an extension fieldMathworldPlanetmath of F. We say that K is a finite extensionMathworldPlanetmath 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 extensionMathworldPlanetmath.

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