PlanetMath (more info)
 Math for the people, by the people. Sponsor PlanetMath
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
Owner confidence rating: High Entry average rating: No information on entry rating
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.
(view preamble | get metadata)

View style:

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
equivalent conditions for normality of a field extension (Theorem) by azdbacks4234
Log in to rate this entry.
(view current ratings)

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

Pending Errata and Addenda
None.
[ View all 1 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)