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Homenormal extension

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# normal extension

A field extension $K/F$ is *normal* if every irreducible polynomial $f\in F[x]$ which has at least one root in $K$ splits (factors into a product of linear factors) in $K[x]$.

An extension $K/F$ of finite degree is normal if and only if there exists a polynomial $p\in F[x]$ such that $K$ is the splitting field for $p$ over $F$.

Related:

SplittingField

Synonym:

normal

Type of Math Object:

Definition

Major Section:

Reference

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