Timeline for Showing that the stable module category of a ring $R$ restricted to maximal Cohen-Macaulay objects is trivial if $\text{gldim } R < \infty$
Current License: CC BY-SA 3.0
12 events
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| Aug 12, 2015 at 19:20 | comment | added | lokodiz | @JasonStarr: Sorry, I got confused by the fact that $\text{pdim}_{\Bbbk[x]} \Bbbk [x]/\langle x^2 \rangle = \infty$. | |
| Aug 12, 2015 at 18:07 | comment | added | Jeremy Rickard | In the non-commutative case I'm not sure whether every map from an $MCM$ module to a module of finite injective dimension factors through a projective module. I don't think the argument in my answer generalizes straightforwardly to prove this, but I'll think about it. | |
| Aug 12, 2015 at 15:10 | history | edited | Jason Starr | CC BY-SA 3.0 |
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| Aug 12, 2015 at 15:03 | history | edited | Jason Starr | CC BY-SA 3.0 |
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| Aug 12, 2015 at 14:47 | comment | added | Jason Starr | @Simon: So that I understand, are you hypothesizing that $R$ has finite injective dimension as an $R$-module (the usual definition of Gorenstein), or are you hypothesizing that every $R$-module has finite injective dimension? Certainly $R=k[x]/\langle x^2\rangle$ has finite injective dimension as an $R$-module: it is an injective $R$-module. | |
| Aug 12, 2015 at 14:41 | history | edited | Jason Starr | CC BY-SA 3.0 |
Added hypothesis on injective dimension.
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| Aug 12, 2015 at 14:37 | comment | added | lokodiz | Isn't $\text{gldim } \Bbbk[x]/\langle x^2 \rangle = \infty$? | |
| Aug 12, 2015 at 14:26 | history | edited | Jason Starr | CC BY-SA 3.0 |
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| Aug 12, 2015 at 14:03 | history | edited | Jason Starr | CC BY-SA 3.0 |
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| Aug 12, 2015 at 13:57 | history | edited | Jason Starr | CC BY-SA 3.0 |
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| S Aug 12, 2015 at 13:50 | history | answered | Jason Starr | CC BY-SA 3.0 | |
| S Aug 12, 2015 at 13:50 | history | made wiki | Post Made Community Wiki by Jason Starr |