By Lemma 10.86.1, we get that is exact. By Artin-Rees lemma, . Therefore we get is exact as required.

]]>Consider a presentation of module M (which is f.g. by assumption) We get that is exact. (Here is viewed as a submodule of .) One sees this by observing that maps surjectively onto .

By Lemma 10.86.1, we get that is exact. By Artin-Rees lemma, Therefore we get is exact as required.

**A correction in the proof of Lemma 10.96.2:**

Here I think you mean an arbitrary ideal in R (and not specifically the ideal w.r.t. which is completed): .

]]>