A pure subalgebra of a finitely generated algebra is finitely generated

Hashimoto, Mitsuyasu

doi:10.1090/S0002-9939-05-07967-0

A pure subalgebra of a finitely generated algebra is finitely generated
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by Mitsuyasu Hashimoto PDF

Proc. Amer. Math. Soc. 133 (2005), 2233-2235 Request permission

Abstract:

We prove the following. Let $R$ be a Noetherian commutative 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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