Field extension

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

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. Archived from the original on 2021-09-15. Retrieved 2021-09-15.

[1] "Extension of a field - Encyclopedia of Mathematics". encyclopediaofmath.org. Archived from the original on 2021-09-15. Retrieved 2021-09-15.

Field extension

Algebraic over k

References

Algebraic over $k$