PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (213)
Orphanage
Unclass'd (1)
Unproven (473)
Corrections (39)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: Medium Entry average rating: No information on entry rating
finite extension (Definition)

Let $ K$ an extension field of $ F$. We say that $ K$ is a finite extension if $ [K:F]$ is finite. That is, $ K$ is a finite dimensional space over $ F$.

An important result on finite extensions establishes that any finite extension is also an algebraic extension.



"finite extension" is owned by drini. [ owner history (1) ]
(view preamble)

View style:

See Also: extension field, algebraic, existence of the minimal polynomial, algebraic extension, the field extension $\mathbb{R}/\mathbb{Q}$ is not finite, algebraic sum and product

Other names:  finite field extension
Keywords:  Galois Theory, Field

Attachments:
a finite extension of fields is an algebraic extension (Theorem) by alozano
Log in to rate this entry.
(view current ratings)

Cross-references: algebraic extension, finite dimensional, extension field
There are 32 references to this entry.

This is version 5 of finite extension, born on 2001-11-08, modified 2003-05-21.
Object id is 708, canonical name is FiniteExtension.
Accessed 5725 times total.

Classification:
AMS MSC: 12F05 (Field theory and polynomials :: Field extensions :: Algebraic extensions)
Pending Errata and Addenda
None.
[ View all 2 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

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