Timeline for Galois connections
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 8, 2013 at 5:20 | comment | added | James Propp | @Jerome: Oh no -- a mistake in the very first paragraph of my article! Ah well; thanks for catching this error. I will fix it once I get LaTeX properly installed on my new Mac and can create pdfs again. | |
| Jan 24, 2013 at 1:20 | comment | added | Jérôme JEAN-CHARLES | @jim It is a detail : in galois.pdf the property is symetric (not reflexive as given). | |
| Aug 2, 2011 at 2:44 | vote | accept | James Propp | ||
| Aug 2, 2011 at 2:43 | vote | accept | James Propp | ||
| Aug 2, 2011 at 2:43 | |||||
| Jul 29, 2011 at 23:28 | comment | added | Qiaochu Yuan | @James: there's nothing to worry about. The closed sets of the corresponding closure operators turn out to be subgroups and subfields. | |
| Jul 29, 2011 at 20:37 | answer | added | Todd Trimble | timeline score: 6 | |
| Jul 29, 2011 at 19:51 | comment | added | James Propp | My problem is, I was inclined to let $A$ and $B$ respectively be the power sets of $E$ and Gal($E/K$), rather than the set of subfields of $E$ and the set of subgroups of Gal($E/K$) (as is standard), and I want to know if there are pitfalls here that I'm not noticing. It seems to me that for any subset $S$ of $E$, the elements of Gal($E/K$) that fix $S$ form a subgroup of Gal($E/K$), and conversely, for any subset $T$ of Gal($E/K$), the elements of $E$ that are fixed by $T$ form a subfield of $E$. So I don't see anything to worry about. But there may be technicalities I'm not seeing. | |
| Jul 29, 2011 at 17:48 | comment | added | Qiaochu Yuan | I'm not sure what you mean by "problem." | |
| Jul 29, 2011 at 17:15 | comment | added | Pace Nielsen | Just skimming through your article, I don't see a connection between individual homomorphisms and individual elements. Rather, the binary relation is between individual field homomorphisms and sets of elements (under the usual partial-ordering by the subset relation). The fixed sets are fields, as you say. | |
| Jul 29, 2011 at 16:45 | history | asked | James Propp | CC BY-SA 3.0 |