A pure subalgebra of a finitely generated algebra is finitely generated
classification
🧮 math.AC
math.AG
keywords
finitelygeneratedalgebrapuresubalgebrafollowingnoetherianprove
read the original abstract
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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