Tag Archives: completions

Commutative Algebra 55

Posted on May 13, 2020 by limsup

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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Commutative Algebra 54

Posted on May 12, 2020 by limsup

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 , , , , , , | 5 Comments