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normal extension (Definition)

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$.



"normal extension" is owned by djao.
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See Also: splitting field

Other names:  normal

Attachments:
example of normal extension (Example) by alozano
example of an extension that is not normal (Example) by Wkbj79
normal is not transitive (Definition) by Wkbj79
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Cross-references: splitting field, polynomial, degree, extension, product, factors, root, irreducible polynomial, field extension
There are 13 references to this entry.

This is version 6 of normal extension, born on 2002-01-05, modified 2006-11-30.
Object id is 1310, canonical name is NormalExtension.
Accessed 7994 times total.

Classification:
AMS MSC12F10 (Field theory and polynomials :: Field extensions :: Separable extensions, Galois theory)

Pending Errata and Addenda
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