Exercise 111.62.1 (Definitions). Provide brief definitions of the italicized concepts.

a

*constructible subset*of a Noetherian topological space,the

*localization*of an $R$-module $M$ at a prime $\mathfrak p$,the

*length*of a module over a Noetherian local ring $(A, \mathfrak m, \kappa )$,a

*projective module*over a ring $R$, anda

*Cohen-Macaulay*module over a Noetherian local ring $(A, \mathfrak m, \kappa )$.

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