Timeline for Domains $D$ for which for any prime $P$, $D_P$ is a PID
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Jan 1, 2014 at 8:35 | vote | accept | Robert M | ||
| Dec 30, 2013 at 21:57 | comment | added | Jesse Elliott | A local ring is Dedekind if and only if it is a DVR if and only if it is a PID. | |
| Dec 30, 2013 at 15:23 | comment | added | user1437 | It's not hard to see that the rings mentioned in the question are Prüfer domains, since the image of any ideal (and hence image of every f.g. ideal) is principal, so every f.g. ideal is invertible, hence Prüfer. However, the rings defined in paper by Gilmer are those for which the localisation at every maximal ideal is Dedekind, not principal, and I can't immediately see why these are equivalent, so the class in this answer is potentially more general. Can anyone explain this or offer a counterexample? | |
| Dec 30, 2013 at 11:33 | history | edited | Chris Wuthrich | CC BY-SA 3.0 |
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| Dec 30, 2013 at 10:04 | history | edited | Jesse Elliott | CC BY-SA 3.0 |
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| Dec 30, 2013 at 8:40 | history | edited | Jesse Elliott | CC BY-SA 3.0 |
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| Dec 30, 2013 at 8:34 | history | answered | Jesse Elliott | CC BY-SA 3.0 |