Difference between revisions of "Field extension"
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If <math>K</math> and <math>L</math> are [[field]]s and <math>K\subseteq L</math>, then <math>L/K</math> is said to be a '''field extension'''. We sometimes say that <math>L</math> is a field extension of <math>K</math>. | If <math>K</math> and <math>L</math> are [[field]]s and <math>K\subseteq L</math>, then <math>L/K</math> is said to be a '''field extension'''. We sometimes say that <math>L</math> is a field extension of <math>K</math>. | ||
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| + | If <math>L/K</math> is a field extension, then <math>L</math> may be thought of as a [[vector space]] over <math>K</math>. The dimension of this vector space is called the ''degree'' of the extension, and is denoted by <math>[L:K]</math>. | ||
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[[Category:Definition]] | [[Category:Definition]] | ||
Revision as of 21:37, 4 May 2008
If 
and 
are fields and 
, then 
is said to be a field extension. We sometimes say that is a field extension of .
If is a field extension, then may be thought of as a vector space over . The dimension of this vector space is called the degree of the extension, and is denoted by ![$[L:K]$](http://latex.artofproblemsolving.com/e/0/2/e02cf56d70606ad14a4a8339c69dbf5eb8fdc7ff.png)
.
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