A pure subalgebra of a finitely generated algebra is finitely generated

preprint2004arXivOpen access

We prove the following. Let $R$ be a Noetherian ring, $B$ a finitely generated $R$ -algebra, and $A$ a pure $R$ -subalgebra of $B$ . Then $A$ is finitely generated over $R$ .

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A pure subalgebra of a finitely generated algebra is finitely generated

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