Timeline for Symbolic powers in regular local rings
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 18, 2011 at 13:39 | vote | accept | Ajay Patwardhan | ||
| May 18, 2011 at 12:14 | answer | added | Sean Sather-Wagstaff | timeline score: 4 | |
| May 18, 2011 at 7:02 | answer | added | user13113 | timeline score: 3 | |
| May 18, 2011 at 6:33 | comment | added | pinaki | To expand on Keerthi's comment: The Auslander–Buchsbaum theorem (en.wikipedia.org/wiki/Auslander-Buchsbaum_theorem) states that every regular local ring is a unique factorization domain. In fact, it is sort of amusing that you can use this result to prove the Auslander-Buchsbaum theorem - since if $p^{(m)} \subseteq p^{(m)}m$, then by Nakayama's lemma $p^{(m)}= 0$, which implies that $p=0$! | |
| May 18, 2011 at 6:11 | comment | added | user13113 | For readers like myself who haven't seen the notation before, $\mathfrak{p}^{(m)}$ is defined as $R \cap \mathfrak{p}^m R_\mathfrak{p}$ | |
| May 18, 2011 at 6:04 | comment | added | Keerthi Madapusi | $R$ is a domain; the only associated prime is $(0)$. | |
| May 18, 2011 at 4:51 | history | asked | Ajay Patwardhan | CC BY-SA 3.0 |