Timeline for Injective indecomposable modules over Laurent polynomial rings
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 24, 2018 at 18:58 | history | edited | Uriya First | CC BY-SA 4.0 |
added 25 characters in body
|
| Oct 24, 2018 at 18:47 | comment | added | Benjamin Steinberg | thanks! That is what I was looking for. I | |
| Oct 24, 2018 at 18:46 | vote | accept | Benjamin Steinberg | ||
| Oct 24, 2018 at 18:23 | comment | added | Uriya First | @BenjaminSteinberg The difference is indeed superfluous. I added an answer to your question about whether the dimension is countable (it is). | |
| Oct 24, 2018 at 18:19 | history | edited | Uriya First | CC BY-SA 4.0 |
added 1909 characters in body
|
| Oct 24, 2018 at 18:00 | comment | added | Benjamin Steinberg | by the way I think the slight difference is superfluous since localization is exact and so localizing $(K/P)$ at $P$ amounts to first localizing $K$ at $P$ and $P$ at $P$ and then moding out, but localizing $K$ at $P$ does nothing. | |
| Oct 24, 2018 at 17:25 | comment | added | Benjamin Steinberg | My real interest is in the dimension over $\mathbb C$. Maybe some parentheses on the localization might help. I have plus one but I really would like to see a prufer group like description in this particular case preferably with a basis over $\mathbb C$. I will add that to the question to be clear. | |
| Oct 24, 2018 at 17:18 | comment | added | Uriya First | @Benjamin You are correct in your understanding, with the slight difference that only the $R$-module$P$ is localized at the prime ideal $P$. (Localizing $K$ at $P$ gives back $K$.) I agree that this is not as explicit as in the case $R=\mathbb{Z}$ mentioned in the comments. I will think more about it. | |
| Oct 24, 2018 at 17:06 | comment | added | Benjamin Steinberg | I’m having trouble parsing this. Do I view K,P as R-modules, take the quotient $K/P$ as an R-module and then localize at P? Is it easy to see what this amounts to concretely? In my original example what I really want to know is whether the injective indecomposables can have countable dimension over $\mathbb C$ so I was hoping for something more explicit. | |
| Oct 24, 2018 at 16:20 | history | answered | Uriya First | CC BY-SA 4.0 |