Transcendental Extension

An extension field of a field F that is not algebraic over F, i.e., an extension field that has at least one element that is transcendental over F.

For example, the field of rational functions F(x) in the variable x is a transcendental extension of F since x is transcendental over F. The field R of real numbers is a transcendental extension of the field Q of rational numbers, since pi is transcendental over Q.

See also

This entry contributed by Margherita Barile

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Barile, Margherita. "Transcendental Extension." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/TranscendentalExtension.html

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