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 22:37, 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
.
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