Anextension field of afield that is notalgebraic over, i.e., anextension field that has at least one element that is transcendental over.

For example, the field of rational functions in the variable is a transcendental extension of since is transcendental over. The field of real numbers is a transcendental extension of the field of rational numbers, since is transcendental over.

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This entry contributed byMargheritaBarile

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Barile, Margherita. "Transcendental Extension." FromMathWorld--A Wolfram Resource, created byEric W. Weisstein.https://mathworld.wolfram.com/TranscendentalExtension.html

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