Field extension

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

The notation $K/k$ means that $K$ is an extension of the field $k$ .

$K$ is sometimes called an overfield of the field $k$ .

Algebraic over $k$

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

References

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

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

Field extension

Algebraic over k {\displaystyle k}

References

Algebraic over $k$