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Tag Archives: completions
Commutative Algebra 55
Exactness of Completion Throughout this article, A denotes a filtered ring. Proposition 1. Let be a short exact sequence ofÂ Amodules. Suppose M is filtered, inducing filtrations on N and P. Then is also exact as modules. Proof Without loss of … Continue reading
Posted in Advanced Algebra
Tagged aadic filtrations, artinrees lemma, blowup algebras, completions, filtrations, limits, noetherian
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Commutative Algebra 54
Filtered Rings Definition. Let A be a ring. A filtration on A is a sequence of additive subgroups such that for any . A filtered ring is a ring with a designated filtration. Note Since , in fact each is … Continue reading
Posted in Advanced Algebra
Tagged completions, filtrations, formal power series, limits, metric spaces, padic, ultrametric
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