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

the

*local ring of $R$ at a prime $\mathfrak p$*,a

*finite*$R$-module,a

*finitely presented*$R$-module,$R$ is

*regular*,$R$ is

*catenary*,$R$ is

*Cohen-Macaulay*.

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