Field extension

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A field extension  is a field containing a given field  as a subfield.[1]

The notation means that  is an extension of the field .

is sometimes called an overfield of the field .

Algebraic over [change | change source]

An element of the field  is called algebraic over  if it satisfies some algebraic equation with coefficients in , and transcendental otherwise.

References[change | change source]

  1. "Extension of a field - Encyclopedia of Mathematics". encyclopediaofmath.org. Retrieved 2021-09-15.