Timeline for Results from abstract algebra which look wrong (but are true)
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 22, 2023 at 11:59 | comment | added | Carl-Fredrik Nyberg Brodda | @HJRW AL’s and Guba’s proofs in the monoid case are both very short and also go via the Hilbert basis theorem. | |
| Jan 22, 2023 at 11:22 | comment | added | HJRW | @ADL: for free groups at least, (not sure about monoids) this is an easy consequence of Hilbert’s basis theorem, so is much older than either GAL or even Makanin. | |
| Jan 20, 2023 at 19:55 | comment | added | Carl-Fredrik Nyberg Brodda | @ADL I see what you mean now, and yes, I definitely agree! (And: hello! I didn't realise it was you until I clicked your profile!) | |
| Jan 20, 2023 at 16:23 | comment | added | ADL | Sorry, wasn't quite thinking correctly - the Guba/Albert-Lawrence result means that the nice descriptions of solutions sets, via Makanin-Razborov diagrams and as EDT0L languages, hold for all systems of equations, rather than just finite systems. | |
| Jan 20, 2023 at 16:12 | history | edited | Carl-Fredrik Nyberg Brodda | CC BY-SA 4.0 | deleted 11 characters in body |
| Jan 20, 2023 at 16:09 | comment | added | Carl-Fredrik Nyberg Brodda | @ADL While I agree that the work by Albert-Lawrence and Guba is remarkable, Makanin’s work predates them, so I’m not sure what the “underlying” part refers to. | |
| Jan 20, 2023 at 16:02 | comment | added | ADL | There is a remarkable fact underlying this work, which is possibly worthy of its own answer: Every system of equations over a free monoid/free group having a finite number of variables is equivalent to a finite subsystem of it. This was the Ehrenfeucht conjecture, proven by Albert-Lawrence and Guva in the 1980s. | |
| Jan 20, 2023 at 15:57 | history | edited | Carl-Fredrik Nyberg Brodda | CC BY-SA 4.0 | deleted 1 character in body |
| S Jan 20, 2023 at 15:42 | history | answered | Carl-Fredrik Nyberg Brodda | CC BY-SA 4.0 | |
| S Jan 20, 2023 at 15:42 | history | made wiki | Post Made Community Wiki by Carl-Fredrik Nyberg Brodda |