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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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## Recent Activity

Oct 21

new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag