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edited Sep 13, 2023 at 15:02

YCor

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Is the projective dimension of finite torsion free-free modules over regular ring of dimension $n$ smaller that $n$?

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asked Sep 13, 2023 at 12:48

Stabilo

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Is the projective dimension of finite torsion free modules over regular ring of dimension $n$ smaller that $n$?

Let $R$ be a Noetherian regular integral domain of Krull dimension $n$. Let $M$ be a finite torsion-free $R$-module. Is this true that $M$ has projective dimension $<n$ ?

This would be a generalization of the fact that finite torsion-free modules over Dedekind rings are projective.