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Tag Archives: completion
Commutative Algebra 57
Continuing from the previous article, A denotes a noetherian ring and all Amodules are finitely generated. As before all completions are taken to be stable for a fixed ideal . Noetherianness We wish to prove that the adic completion of … Continue reading
Posted in Advanced Algebra
Tagged aadic filtrations, algebraic geometry, analysis, completion, filtrations, hensels lemma, local rings, padic
1 Comment
Commutative Algebra 56
Throughout this article, A denotes a noetherian ring and is a fixed ideal. All Amodules are finitely generated. Consequences of ArtinRees Lemma Suppose we have an exact sequence of finitely generated Amodules Let M be given the 𝔞adic filtration; the induced filtration on … Continue reading
Topology: Complete Metric Spaces
[ This article was updated on 8 Mar 13; the universal property is now in terms of Cauchycontinuous maps. ] On an intuitive level, a complete metric space is one where there are “no gaps”. Formally, we have: Definition. A … Continue reading
Posted in Notes
Tagged advanced, cauchy sequences, complete metric spaces, completion, metric spaces, topology, universal properties
10 Comments