Timeline for Primary decomposition for modules
Current License: CC BY-SA 3.0
12 events
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| S Jun 5, 2017 at 19:43 | history | suggested | user 1 |
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| Jun 5, 2017 at 19:31 | review | Suggested edits | |||
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| S Jun 5, 2017 at 9:02 | history | suggested | user 1 | CC BY-SA 3.0 |
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| Jun 5, 2017 at 7:52 | review | Suggested edits | |||
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| Aug 24, 2012 at 1:50 | comment | added | Charles Staats | As an additional note, the definition Matsumura gives in Commutative Ring Theory (a different book from Commutative Algebra) agrees with the Atiyah-Macdonald definition. That these two definitions are not equivalent, even for a noetherian base ring, can be seen by considering the $\mathbb Z$-module $\bigoplus_n \mathbb Z / p^n$, which is coprimary only by the weaker definition. | |
| Aug 24, 2012 at 1:45 | comment | added | Charles Staats | Personally, I think the notion of "coprimary module" is more important than the notion of "primary submodule." For non-finitely-generated modules over noetherian rings, the right notion of coprimary seems to be that $M$ is coprimary if it has exactly one associated prime. (This gets used in classifying injective modules.) $N \subset M$ is primary if $M/N$ is coprimary. By this definition, a module is coprimary iff all of its finitely generated submodules are; consequently, it agrees with the definition from Matsumura's Commutative Algebra. | |
| Aug 23, 2012 at 15:55 | comment | added | David Corwin | Note: the decision to edit this question was based in part on this meta thread: tea.mathoverflow.net/discussion/1431/… | |
| Aug 23, 2012 at 15:54 | history | edited | David Corwin | CC BY-SA 3.0 |
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| Mar 8, 2010 at 15:38 | answer | added | Andrea Ferretti | timeline score: 1 | |
| Nov 3, 2009 at 9:30 | history | edited | Ilya Nikokoshev |
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| Nov 3, 2009 at 7:44 | answer | added | Greg Stevenson | timeline score: 4 | |
| Nov 3, 2009 at 7:05 | history | asked | user709 | CC BY-SA 2.5 |