Timeline for Is every Noetherian Commutative Ring a quotient of a Noetherian Domain?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 10, 2014 at 21:47 | vote | accept | Siddharth Venkatesh | ||
| Apr 3, 2014 at 21:16 | answer | added | Jérôme Poineau | timeline score: 13 | |
| Apr 2, 2014 at 14:33 | answer | added | user46855 | timeline score: 37 | |
| Apr 2, 2014 at 1:18 | comment | added | Julian Rosen | @Joël The ring $\mathbb{Q}\times\mathbb{F}_p$ is the image of the Noetherian domain $\mathbb{Z}_{(p)}[x]$ under the map sending $x$ to $(1/p,0)$. | |
| Apr 2, 2014 at 0:16 | comment | added | Joël | This might be stupid, but does anyone here can show that $\mathbb Q \times \mathbb F_p$ is the quotient of a Noetherian domain? What are examples of Noetherian domains which are not $\mathbb Q$-algebras but admit $\mathbb Q$ as a quotient? | |
| Apr 2, 2014 at 0:04 | comment | added | David E Speyer | Oh, I see. Regular for you means that all local rings are regular local rings (of some finite Krull dimension). That makes a lot of sense. I'm used to defining "regular of dimension $d$" to mean local rings at maximal primes are regular of dimension $d$, and then "regular" means "regular of some dimension". | |
| Apr 1, 2014 at 19:07 | comment | added | Siddharth Venkatesh | I think the notion of regular I'm using just involves the hypothesis that the localization at each prime is a regular local ring, which is well-defined even in the absence of finite Krull-Dimension because each localization is finite Krull-Dimension. So Nagata's example is something I would call regular in the problem but I'm not sure what statement of the problem it violates. Could you elaborate a little on that please? | |
| Apr 1, 2014 at 15:45 | comment | added | David E Speyer | I am a little confused about your second part. I usually understand regular to include finite Krull dimension, in which case Nagata's example mathoverflow.net/questions/21067/… violates at least the second statement of your second part. But it sounds like you have a broader definition of regular in mind? | |
| Apr 1, 2014 at 6:23 | history | asked | Siddharth Venkatesh | CC BY-SA 3.0 |