Zariski's finiteness theorem

In algebra, Zariski's finiteness theorem gives a positive answer to Hilbert's 14th problem for the polynomial ring in two variables, as a special case. Precisely, it states:

Given a normal domain A, finitely generated as an algebra over a field k, if L is a subfield of the field of fractions of A containing k such that ${\mathrm{tr.deg}}_k(L)\le 2$, then the k-subalgebra $L\cap A$ is finitely generated.

References

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