Timeline for Is it true that this ideal must be principal? (proof verification)
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 16, 2021 at 14:14 | history | protected | Tim Campion | ||
| Jul 10, 2021 at 16:28 | vote | accept | CommunityBot | ||
| Jul 10, 2021 at 13:06 | answer | added | AlexIvanov | timeline score: 9 | |
| Jul 9, 2021 at 17:59 | comment | added | user106850 | @hans point taken, I edited the question. And no, as $\beta$ is not necessarily integral. It could be that $(\beta) = \mathfrak{P}I/\sigma(I)$, then we still have $(\beta \sigma(\beta)) = \mathfrak{P} \sigma(\mathfrak{P}).$ | |
| Jul 9, 2021 at 17:57 | history | edited | user106850 | CC BY-SA 4.0 |
Use $\mathfrak{P}$ for the big field
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| Jul 9, 2021 at 17:56 | comment | added | hans | If $\beta \sigma(\beta) \mathcal{O}_L = \mathfrak{P}\sigma({\mathfrak{P}})$, doesn't it follow from the unique factorization that either $\beta = \mathfrak{P}$ or $\sigma(\beta) = \mathfrak{P}$? | |
| Jul 9, 2021 at 17:53 | comment | added | hans | It is a bit confusing to use $\mathfrak{p}$ for the prime ideal in the big field. | |
| Jul 9, 2021 at 17:44 | history | asked | user106850 | CC BY-SA 4.0 |