Now we have a Noetherian ring that isn’t Nagata and isn’t Grothendieck thanks to KReiser. Based on the comment in wikipedia that these were “hard to find” I thought it would be very pathological, but as it turns out, it is a discrete valuation ring and not very hard to describe. That’s definitely a plus, because the missing quality is demonstrated to be not attributable to some weird structure of the ring.
A recent bundle of JeremyRickard’s suggestions resulted not only in marked improvement for Ring 57, but also resulted in the detection of two missing bits of logic. When those were added and the dust settled, well over 100 more ring-property relationships were decided. Sometimes it’s hard to estimate what your suggestion’s impact will be!
It recently came to my attention that a user experienced a 500 server error on the site. It turns out a piece of infrastructure shifted out from under me to cause the issue, but now I’ve got it fixed.
If you think you might need some help resolving some problem related to a 500 on the DaRT site, just comment here and I’ll see what I can do!
Today I filled in the description of an example in a paper by McGovern which is a potent ring that isn’t clean. It’s a case where we have a ring of continuous real valued functions where the ring-theoretic properties are linked to the topological properties of the space.
I added an example due to Akizuki of a Noetherian local domain that isn’t a Nagata ring. From what I’ve read, Nagata rings are considered “geometrically nice,” and there was some hope that all Noetherian domains were nice too, but this example dashed those hopes.
I included both because they were “easy” enough to describe, and interesting, but unfortunately I do not know of any properties that would distinguish the two, at the moment. If you can find any… let me know!
MatheinBoulomenos recently left seven separate suggestions for adding a property or two to rings, and fill out a few metaproperties of properties. All together these blossomed to 70 new properties being decided (split among various rings) owing to the site software.
This is a great reminder of how your contribution might have a bigger impact than you can predict!
Thanks JoseBrox for finding a ring with the ACC on annihilators on only one side, and also KReiser for suggesting an example of Nagata’s of a normal domain which isn’t analytically normal.
This is also the first test of my new feed setup… I hope everyone approves!
Previously I had only disseminated news and announcements in an RSS feed on the site. This blog is intended to upgrade that by leaving space for bigger posts, and also allowing you to subscribe via email!
Don’t worry, if you’re like me and still like RSS even if it’s old and uncool, you can still keep the same feed address on the site: I’ll just forward it to the feed that WordPress provides to this site!
Hopefully this gives you readers more options and more ways to share what we’re doing here at DaRT. Thanks for reading!