Timeline for Exotic principal ideal domains
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Jun 22, 2022 at 8:13 | history | edited | CommunityBot |
replaced http://math.uga.edu/~pete with http://alpha.math.uga.edu/~pete
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| Jan 10, 2019 at 8:58 | comment | added | Matthieu Romagny | Dear Pete, do you have a reason to link to commutative algebra notes (integral.pdf) different from those one finds on your webpage (integral2015.pdf) ? | |
| Jan 10, 2019 at 6:35 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
corrected link - it was hidden under proxy
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| May 16, 2011 at 13:40 | vote | accept | Qiaochu Yuan | ||
| Feb 24, 2011 at 17:48 | comment | added | Pete L. Clark | @JSE: Really? Do I use the word "finicky" a lot? Or is it just the kind of word I would use? (If so, you must know me pretty well...) | |
| Feb 24, 2011 at 16:42 | comment | added | JSE | As soon as I saw the word "finicky" I knew this was one of yours, Pete. | |
| Feb 24, 2011 at 16:11 | comment | added | Qiaochu Yuan | Agh, yes, what I meant to say was "all the Bezout domains I care about are Noetherian anyway." | |
| Feb 24, 2011 at 15:44 | comment | added | Chris Eagle | All PIDs are Noetherian. A Bezout domain is Noetherian iff it is a PID. | |
| Feb 24, 2011 at 15:30 | comment | added | Qiaochu Yuan | I see. I suppose all the PIDs I care about are Noetherian anyway, so I am totally okay with taking the perspective that Bezout domains are the more fundamental concept. | |
| Feb 24, 2011 at 15:18 | comment | added | Emil Jeřábek |
With regards to Bézout domains that are not (elementary submodels of) unltraproducts of PIDs, an example which I think is easier to verify is $R=\bigcup_nF[x^{1/n}]$, where $F$ is a field. $R$ is Bézout because any its finitely generated subring is contained in some $F[x^{1/n}]$, which is a PID. OTOH, $x$ is not a unit in $R$, but it has no prime divisor.
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| Feb 24, 2011 at 15:10 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
added 260 characters in body
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| Feb 24, 2011 at 15:05 | history | answered | Pete L. Clark | CC BY-SA 2.5 |