simple transcendental field extension

The extension fieldMathworldPlanetmath K(α) of a base fieldMathworldPlanetmath K, where α is a transcendental element with respect to K, is a simple ( transcendental extensionMathworldPlanetmath of K.  All such extension fields are isomorphic to the field K(X) of rational functions in one indeterminateMathworldPlanetmath X over K, and thus to each other.

Example.  The subfieldsMathworldPlanetmath (π) and (e) of , where π is Ludolph’s constant ( and e Napier’s constant, are isomorphic.

Title simple transcendental field extension
Canonical name SimpleTranscendentalFieldExtension
Date of creation 2013-03-22 15:02:20
Last modified on 2013-03-22 15:02:20
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 11
Author pahio (2872)
Entry type Corollary
Classification msc 12F99
Synonym simple infinite field extension
Related topic FunctionField