Difference between revisions of "Field extension"

(Defined the degree of an 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 $K$ and $L$ are fields and $K\subseteq L$, then $L/K$ is said to be a field extension. We sometimes say that $L$ is a field extension of $K$.

If $L/K$ is a field extension, then $L$ may be thought of as a vector space over $K$. The dimension of this vector space is called the degree of the extension, and is denoted by $[L:K]$.

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