The degree (or relative degree, or index) of an extension field 
,
denoted ![[K:F]](/images/equations/ExtensionFieldDegree/Inline2.svg)
,
is the dimension of 
as a vector space over 
, i.e.,
![[K:F]=dim_FK.](/images/equations/ExtensionFieldDegree/NumberedEquation1.svg) |
If ![[K:F]](/images/equations/ExtensionFieldDegree/Inline5.svg)
is finite, then the extension is said to be finite; otherwise, it is said to be infinite.
Extension Field Degree
See also
Extension FieldExplore with Wolfram|Alpha
References
Dummit, D. S. and Foote, R. M. "Basic Theory of Field Extensions." §13.1 in Abstract Algebra, 3rd ed. Hoboken, NJ: Wiley, pp. 510-519, 2004.Referenced on Wolfram|Alpha
Extension Field DegreeCite this as:
Weisstein, Eric W. "Extension Field Degree." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ExtensionFieldDegree.html