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Extension Field Degree


The degree (or relative degree, or index) of an extension field K/F, denoted [K:F], is the dimension of K as a vector space over F, i.e.,

 [K:F]=dim_FK.

If [K:F] is finite, then the extension is said to be finite; otherwise, it is said to be infinite.


See also

Extension Field

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References

Dummit, D. S. and Foote, R. M. Abstract Algebra, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, p. 424, 1998.

Referenced on Wolfram|Alpha

Extension Field Degree

Cite this as:

Weisstein, Eric W. "Extension Field Degree." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ExtensionFieldDegree.html

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