Tag Archives: artin-rees lemma

Commutative Algebra 56

Throughout this article, A denotes a noetherian ring and is a fixed ideal. All A-modules are finitely generated. Consequences of Artin-Rees Lemma Suppose we have an exact sequence of finitely generated A-modules Let M be given the 𝔞-adic filtration; the induced filtration on … Continue reading

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Commutative Algebra 55

Exactness of Completion Throughout this article, A denotes a filtered ring. Proposition 1. Let be a short exact sequence of A-modules. Suppose M is filtered, inducing filtrations on N and P. Then is also exact as -modules. Proof Without loss of … Continue reading

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