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If ''L'' is an extension of ''F'', which is in turn an extension of ''K'', then ''F'' is said to be an '''intermediate field''' (or '''intermediate extension''' or '''subextension''') of <math>L/K</math>.
Given a field extension <math>L/K</math>, the larger field ''L'' is a ''K''-[[vector space]]. The [[dimension (vector space)|dimension]] of this vector space is called the [[degree of a field extension|'''degree''' of the extension]] and is denoted by <math>[
The degree of an extension is 1 if and only if the two fields are equal. In this case, the extension is a '''{{vanchor|trivial extension}}'''. Extensions of degree 2 and 3 are called '''quadratic extensions''' and '''cubic extensions''', respectively. A '''finite extension''' is an extension that has a finite degree.
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