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.