A pure subalgebra of a finitely generated algebra is finitely generated

Details A pure subalgebra of a finitely generated algebra is finitely generated A pure subalgebra of a finitely generated algebra is finitely generated

2004-06-15

arxiv.org/abs/math/0406286v1

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

Mathematics

Commutative Algebra

4 pages

Scientific paper

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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