Timeline for Are topological PID's Noetherian?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Sep 20, 2023 at 12:23 | comment | added | Nik Weaver | @RomainGicquaud: Right. What I need is for the implication to be true for all locally compact, metrizable rings. (But if you figure this out, maybe wait a day before posting, to give me a chance to assign a bounty.) | |
| Sep 20, 2023 at 12:03 | comment | added | Romain Gicquaud | @NikWeaver: You can already rule out the possibility that $R$ is a $\mathbb{R}$-algebra as local compactness will imply that $R$ is a finite dimensional vector space. But for more general rings, I have no clue. Maybe you should precise the kind of applications you have in mind. | |
| Sep 19, 2023 at 15:53 | comment | added | Nik Weaver | Nice! I think this is correct, modulo YCor's adjustment. What if we restrict to locally compact rings? | |
| Sep 19, 2023 at 15:43 | comment | added | YCor | Your assumption on $(z_n)$ is not exactly the right one. Write $Z=\{z_n:n\ge 0\}$ (and assume $n\mapsto z_n$ is injective). Your assumption, as now formulated, is that $Z$ is discrete. But the assumption you need is that $Z$ is closed discrete, and this is indeed the case when you write "for example a sequence of points tending to a boundary point". For instance if $z_n$ is a sequence tending to a point of $\Omega$ (not among the $z_n$), then the assertion "there exists a holomorphic..." is not correct. | |
| Sep 19, 2023 at 15:36 | history | answered | Romain Gicquaud | CC BY-SA 4.0 |