The Stacks project

Exercise 111.12.3. Let $(R, \mathfrak m)$ be a local Noetherian domain. Let $M$ be a finite $R$-module.

  1. If $M$ is torsion free, show that $M$ has depth at least $1$ over $R$.

  2. Give an example with depth equal to $1$.

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View Exercise 111.12.3 as pdf