Timeline for Why depth, dimension, etc?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jul 20, 2012 at 21:23 | comment | added | Mikhail Gudim | For me positive (or at least partial) answers to both questions would be an excellent motivation - that's precisely what I am asking for. I think combinatorial condition probably will be very ugly, so maybe look for "topological" one (see my last comment). Maybe I should change the question... | |
| Jul 20, 2012 at 19:35 | comment | added | Hailong Dao | Mikhail: I can sort of see your point now, although still not completely sure. It would be interesting and helpful to really work out what (iii) says combinatorialy and add that to the question. Also, the title is somewhat vague, at first I thought someone was asking for motivations (-: | |
| Jul 20, 2012 at 19:01 | comment | added | Mikhail Gudim | Maybe it would be better to ask the same question but for functions on $Spec R$ as a topological space rather then functions on a poset. I.e. can $Spec R$ be recovered as a topological space from the knowledge of functions $Spec R \to \mathbb N$ satifying properties of theorem 2.4 in McAdam's paper. | |
| Jul 20, 2012 at 18:56 | comment | added | Mikhail Gudim | I thought condition (iii) could be expressed just using the poset. This is why: the poset of prime ideals determines the poset of all radical ideals (by some kind of completion procedure for a poset - this is fishy) Then the fact $Q \subset \cap P$ is equivalent to $rad Q = rad (\cap P)$ and $Q \subset \cap P$ for prime $Q$, so this can also be expressed using just the poset.(I also think that poset of radical ideals determines Zariski topology which in turn determines poset of prime ideals). Anyways... I was hoping that there is a nice combinatorial condition equivalent to that in the paper | |
| Jul 20, 2012 at 16:11 | history | answered | Hailong Dao | CC BY-SA 3.0 |