Timeline for Why is $M$ torsion-free?
Current License: CC BY-SA 4.0
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| Sep 26, 2021 at 20:38 | comment | added | user26857 | I don't know what hypotheses you are assuming in that Lemma, but the converse doesn't hold in general. For instance, for $R=K[X,Y]$ (eventually localized at $(X,Y)$) and $M=R/(XY)$. | |
| Sep 16, 2021 at 17:13 | history | edited | Mare | CC BY-SA 4.0 |
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| Sep 16, 2021 at 16:35 | comment | added | Danimenru | But, to apply the other part it is necessary that R be domain. I dont know if holds when $R$ is not domain (In the article, $R$ is not necessarily a domain | |
| Sep 16, 2021 at 16:26 | comment | added | Mare | @Danimenru Yes, the other part of the propositon 1.5 says that for $d \geq 2$ the MCM modules are even reflexive which implies torsion-free. | |
| Sep 16, 2021 at 16:14 | comment | added | Danimenru | You are using the proposition (1.5.2)? This proposition is valid for d = 1. | |
| Sep 16, 2021 at 16:07 | comment | added | Danimenru | Then, every Maximal Cohen Macaulay module are torsion-free? | |
| Sep 16, 2021 at 16:05 | history | edited | Mare | CC BY-SA 4.0 |
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| Sep 16, 2021 at 15:49 | history | edited | Mare | CC BY-SA 4.0 |
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| Sep 16, 2021 at 15:44 | history | answered | Mare | CC BY-SA 4.0 |