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normal extension
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(Definition)
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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 $F$
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"normal extension" is owned by djao.
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Cross-references: splitting field, polynomial, degree, extension, product, factors, root, irreducible polynomial, field extension
There are 16 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 9995 times total.
Classification:
| AMS MSC: | 12F10 (Field theory and polynomials :: Field extensions :: Separable extensions, Galois theory) |
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Pending Errata and Addenda
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