Timeline for prime ideals in regular local rings
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 14, 2011 at 3:45 | vote | accept | Koose Muniswamy | ||
| Feb 8, 2011 at 19:55 | comment | added | Hailong Dao | @Koose: I am not sure how to reduce to 2-generator case. What I had in mind is pretty simple: if $P=(x_1,\cdots,x_n)$, then my claim shows that $(x_2,\cdots, x_{n})$ is prime. Also, since one can permute reg sequence, all subsets of min. generators of $P$ generate prime ideals. | |
| Feb 8, 2011 at 4:14 | comment | added | Koose Muniswamy | @Hailong: Thanks for the answer. Just to make it completely explicit. If $P$ is a complete intersection in a regular local ring (hence Cohen Macaulay), there is a regular sequence that generates it. We can reduce to case where $P$ is $2$ generator using induction. Then, using your claim and the fact that regular sequences are permutable in a Noetherian local ring, we get the result. Does this sound OK? | |
| Feb 8, 2011 at 2:39 | history | edited | Hailong Dao | CC BY-SA 2.5 |
added 12 characters in body
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| Feb 8, 2011 at 1:49 | history | answered | Hailong Dao | CC BY-SA 2.5 |