nLab transcendental extension

Redirected from "purely transcendental extension".
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Definition

A field extension KLK \subset L is a transcendental (field) extension of KK if there is αL\alpha\in L for which every polynomial function with coefficients in KK is equal to the zero polynomial function if it has α\alpha among its roots when interpreted in LL (in other words, α\alpha is transcendental over KK).

A field extension KLK \subset L is a purely transcendental extension if there is an algebraically independent subset SLS \subseteq L over KK such that K(S)K(S) is isomorphic to LL.

References

Last revised on February 23, 2024 at 22:53:53. See the history of this page for a list of all contributions to it.