simple transcendental field extension
The extension field of a base field , where is a transcendental element with respect to , is a simple (http://planetmath.org/SimpleFieldExtension) transcendental extension of . All such extension fields are isomorphic to the field of rational functions in one indeterminate over , and thus to each other.
Example. The subfields and of , where is Ludolph’s constant (http://planetmath.org/Pi) and Napier’s constant, are isomorphic.
Title | simple transcendental field extension |
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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 |