the field extension / is not finite


Let L/K be a finite field extension. Then L/K is an algebraic extensionMathworldPlanetmath.


The extension of fields R/Q is not finite.

Proof of the Corollary.

If the extension was finite, it would be an algebraic extension. However, the extension / is clearly not algebraic. For example, e is transcendental over (see e is transcendental). ∎

Title the field extension / is not finite
Canonical name TheFieldExtensionmathbbRmathbbQIsNotFinite
Date of creation 2013-03-22 13:57:32
Last modified on 2013-03-22 13:57:32
Owner alozano (2414)
Last modified by alozano (2414)
Numerical id 6
Author alozano (2414)
Entry type Corollary
Classification msc 12F05
Synonym the reals is not a finite extension of the rationals
Related topic Pi
Related topic Algebraic
Related topic FiniteExtension