Timeline for Can any properties of a ring other than being a field be captured by the geometry of its 2-dimensional free module?
Current License: CC BY-SA 4.0
13 events
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| May 16 at 17:41 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| May 16 at 9:02 | history | edited | YCor |
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| Nov 13, 2010 at 3:10 | comment | added | David E Speyer | @Charles Staats -- my answer is more or less what an algebraic geometer would say about this question. As you can see, I'm not sure if it's what the questioner wanted, but it's not completely off topic either. I'd leave the tag. | |
| Nov 12, 2010 at 23:24 | history | edited | Romeo |
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| Nov 12, 2010 at 18:17 | answer | added | David E Speyer | timeline score: 3 | |
| Nov 12, 2010 at 18:03 | answer | added | Marius Buliga | timeline score: 2 | |
| Jul 17, 2010 at 0:35 | comment | added | Charles Staats | I added a "group theory" tag since, to my knowledge, that is where this sort of thing is actually used. I strongly question the use of the "algebraic geometry" tag, but am not certain enough to remove it. | |
| Jul 17, 2010 at 0:34 | history | edited | Charles Staats |
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| Jul 16, 2010 at 21:03 | history | edited | Vladimir Sotirov | CC BY-SA 2.5 |
fixed typo
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| Jul 16, 2010 at 20:56 | comment | added | Jack Schmidt | Instead of understanding rings R via their PGL(2,R), the group theorists understand groups G via their similarity to PGL(2,D). Just like you find the ring, you can find the group from the geometry. Even if you only have a partial knowledge of the group, it may be enough to construct the geometry, and then recognize the group. David Benson and Steven Smith has a reasonably neat book about doing this in the case of sporadic simple groups. | |
| Jul 16, 2010 at 20:52 | comment | added | Jack Schmidt | If your motivating question is "can more like this be done?" then Dembowski's Finite Geometry book is very nice. This sort of geometry uses other field like structures (near-fields) to handle the non-Desarguesian planes, and they are fairly interesting. Hall's Theory of Groups textbook has some of this. Zassenhaus's understanding of non-desarguesian planes was a very important step for finite group theorists, and was part of the path that includes Suzuki's work on exceptional characters, and the Feit-Thompson theorem. | |
| Jul 16, 2010 at 20:41 | history | asked | Vladimir Sotirov | CC BY-SA 2.5 |