Quasiaffines Schema/Affin/Superhöhe 1 und endlich erzeugter Schnittring/en/Fakt

Let ${}R$ be a noetherian commutative ring and let ${}I\subseteq R$ be an ideal and ${}U=D(I)\subseteq X=\operatorname {Spec} {\left(R\right)}$. Then the following are equivalent.

1. ${}U$ is an affine scheme.
2. ${}I$ has superheight ${}\leq 1$ and ${}\Gamma (U,{\mathcal {O}}_{X})$ is a finitely generated ${}R$-algebra.

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