Timeline for Commutation of tensor products with inverse limits in a specific case
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Jan 10, 2021 at 6:43 | comment | added | Duchamp Gérard H. E. | However, I remain interested by the case of rings of analytic functions, if you have insights do not hesitate. | |
| S Mar 21, 2015 at 10:54 | history | suggested | Duchamp Gérard H. E. | CC BY-SA 3.0 |
Replaced [If $M$ is finitely presented then $f_{R,X}$]--->[In case $M$ is finitely presented then $f_{M,Y}$] because of confusion in the letters ($R$ is the ground ring since the beginning).
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| Mar 21, 2015 at 10:40 | review | Suggested edits | |||
| S Mar 21, 2015 at 10:54 | |||||
| Mar 20, 2015 at 5:50 | vote | accept | Duchamp Gérard H. E. | ||
| Mar 20, 2015 at 5:49 | comment | added | Duchamp Gérard H. E. | Considering my title as a context, I wanted you to tell me more which is done now. I however maintain my edit for the sake of clarity (for an external reader) and accept your contribution as answer (in which I learned a lot). | |
| Mar 20, 2015 at 5:27 | comment | added | Duchamp Gérard H. E. | Well, I choosed my words carefully : my first reflex is to see products as inverse and not direct limits. I thought you might have a ``hidden trick'' to consider direct limits here a | |
| Mar 20, 2015 at 1:29 | comment | added | user74230 | @DuchampGérardH.E.: Yes, such rings are not noetherian, and certainly the direct products are not direct limits. But that is not relevant, since I put the problem in the wider generality where the left factor is an arbitrary $R$-module, so it becomes meaningful to consider expressing it as a direct limit of finitely generated submodules. That being said, I wrote my answer specifically without even invoking the notion of direct limit, so I'm not sure what causes you to raise question (a) in your comment. | |
| S Mar 20, 2015 at 0:10 | history | suggested | Duchamp Gérard H. E. | CC BY-SA 3.0 |
I replaced [more effective use direct limits] by [more effective the use of limits]. I fact I think the limit here is inverse and not direct.
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| Mar 19, 2015 at 23:46 | review | Suggested edits | |||
| S Mar 20, 2015 at 0:10 | |||||
| Mar 19, 2015 at 16:51 | comment | added | Duchamp Gérard H. E. | (a) I do not understand (infinite) products as direct but rather as inverse limits can you tell me more ? (b) The ring of entire functions $\mathbb{C}\rightarrow \mathbb{C}$ is unfortunately not noetherian (take the ideals $I_k$ of functions vanishing on $\{k,k+1,k+2,\cdots\}$, it is strictly increasing) ... but (c) I greatly appreciate your generalization of the ``field case'', thanks. | |
| Mar 19, 2015 at 15:25 | comment | added | Duchamp Gérard H. E. | Thank you for your answer, I find it convincing and will redo the details. My primary interest was for $R$ being the ring of analytic (complex) functions on an open domain (which I think is not noetherian). | |
| Mar 19, 2015 at 14:57 | history | answered | user74230 | CC BY-SA 3.0 |