The Stacks project

Exercise 111.58.1 (Definitions). Let $R$ be a ring. Provide definitions of the italicized concepts.

  1. the local ring of $R$ at a prime $\mathfrak p$,

  2. a finite $R$-module,

  3. a finitely presented $R$-module,

  4. $R$ is regular,

  5. $R$ is catenary,

  6. $R$ is Cohen-Macaulay.

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View Exercise 111.58.1 as pdf