Artin-Rees lemma - Revision history

Vipul: 4 revisions

2008-05-12T16:18:34Z

4 revisions

← Older revision	Revision as of 16:18, 12 May 2008
(No difference)

Vipul at 19:55, 3 March 2008

2008-03-03T19:55:10Z

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 {{indispensable lemma}}
 {{Noetherian ring result}}
 ==Statement==
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 is also essentially <math>I</math>-adic.

Vipul at 17:03, 27 February 2008

2008-02-27T17:03:21Z

← Older revision		Revision as of 17:03, 27 February 2008
Line 1:		Line 1:
	{{indispensable lemma}}		{{indispensable lemma}}
			{{Noetherian ring result}}
	==Statement==		==Statement==

Vipul: /* Statement */

2008-02-27T15:50:05Z

Statement

← Older revision		Revision as of 15:50, 27 February 2008
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	<math>M = M_0 \supset M_1 \supset M_2 \supset \ldots</math>		<math>M = M_0 \supset M_1 \supset M_2 \supset \ldots</math>

	is an essentially <math>I</math>-adic filtration (in other words, there exists <math>n_0</math> such that for all <math>n \ge n_0</math>, <math>IM_n = M_{n+1</math>).		is an essentially <math>I</math>-adic filtration (in other words, there exists <math>n_0</math> such that for all <math>n \ge n_0</math>, <math>IM_n = M_{n+1}</math>).

	Then the filtration of <math>N</math> given by:		Then the filtration of <math>N</math> given by:

Vipul: New page: {{indispensable lemma}} ==Statement== Suppose $A$ is a Noetherian commutative unital ring and $M$ is a [[finitely generated module|finitely ...

2008-02-27T15:49:49Z

New page: {{indispensable lemma}} ==Statement== Suppose <math>A</math> is a Noetherian commutative unital ring and <math>M</math> is a [[finitely generated module|finitely ...

New page

{{indispensable lemma}}

==Statement==

Suppose <math>A</math> is a [[Noetherian ring|Noetherian]] [[commutative unital ring]] and <math>M</math> is a [[finitely generated module|finitely generated]] <math>A</math>-[[module]] and <math>N</math> a submodule of <math>M</math>.

Suppose:

<math>M = M_0 \supset M_1 \supset M_2 \supset \ldots</math>

is an essentially <math>I</math>-adic filtration (in other words, there exists <math>n_0</math> such that for all <math>n \ge n_0</math>, <math>IM_n = M_{n+1</math>).

Then the filtration of <math>N</math> given by:

<math>N = N \cap M_0 \supset N \cap M_1 \supset N \cap M_2 \supset \ldots</math>

is also essentially <math>I</math>-adic.

Artin-Rees lemma - Revision history

Vipul: 4 revisions

Vipul at 19:55, 3 March 2008

Vipul at 17:03, 27 February 2008

Vipul: /* Statement */

Vipul: New page: {{indispensable lemma}} ==Statement== Suppose A is a Noetherian commutative unital ring and M is a [[finitely generated module|finitely ...

Vipul: New page: {{indispensable lemma}} ==Statement== Suppose $A$ is a Noetherian commutative unital ring and $M$ is a [[finitely generated module|finitely ...