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 (210)
Orphanage
Unclass'd (1)
Unproven (472)
Corrections (38)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: Very high Entry average rating: No information on entry rating
linearly disjoint (Definition)

Let $ E$ and $ F$ be subfields of $ L$, each containing a field $ K$. $ E$ is said to be linearly disjoint from $ F$ over $ K$ if every subset of $ E$ linearly independent over $ K$ is also linearly independent over $ F$.

Remark. If $ E$ is linearly disjoint from $ F$ over $ K$, then $ F$ is linearly disjoint from $ E$ over $ K$. Then one can speak of $ E$ and $ F$ being linearly disjoint over $ K$ without causing any confusions.



"linearly disjoint" is owned by CWoo.
(view preamble)

View style:

Log in to rate this entry.
(view current ratings)

Cross-references: linearly independent, subset, field, subfields
There is 1 reference to this entry.

This is version 4 of linearly disjoint, born on 2004-04-21, modified 2004-04-22.
Object id is 5793, canonical name is LinearlyDisjoint.
Accessed 1559 times total.

Classification:
AMS MSC: 12F20 (Field theory and polynomials :: Field extensions :: Transcendental extensions)
Pending Errata and Addenda
None.
Discussion
Style: Expand: Order:
forum policy

No messages.

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