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# 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.

Keywords:

Galois Theory, Field

Related:

ExtensionField, AlgebraicElement, ExistenceOfTheMinimalPolynomial, AlgebraicExtension, ExtensionMathbbRmathbbQIsNotFinite, AlgebraicSumAndProduct, FiniteExtensionsOfDedekindDomainsAreDedekind

Synonym:

finite field extension

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

12F05*no label found*

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## Recent Activity

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new correction: Error in proof of Proposition 2 by alex2907

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new correction: Error in proof of Proposition 2 by alex2907

Jun 24

new question: A good question by Ron Castillo

Jun 23

new question: A trascendental number. by Ron Castillo

Jun 19

new question: Banach lattice valued Bochner integrals by math ias

Jun 13

new question: young tableau and young projectors by zmth

Jun 11

new question: binomial coefficients: is this a known relation? by pfb

Jun 6

new question: difference of a function and a finite sum by pfb