Timeline for Absolute Irreducibility in Characteristic 2
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jul 5, 2011 at 0:20 | comment | added | Bruno | Thanks for your comments. Actually, I am working in characteristic 2, so my question was something like "do there exist some specificities of characteristic 2?". Your example rules out the possibility of all absolutely irreducible polynomials to be multilinear. I was convinced there must a simple example, there it is! I'll have a look to Noether's criterion. If somebody has a reference in English, it would be even easier! | |
| Jul 5, 2011 at 0:12 | comment | added | Mariano Suárez-Álvarez | Interesting, it appears that one can test for absolute irreducibility without leaving the initial field, according to [Noether, E., Ein algebraisches Kriterium für absolute Irreduzibilität, Math. Ann. 85, p.26—32 (1922)] | |
| Jul 4, 2011 at 23:33 | comment | added | Mariano Suárez-Álvarez | The polynomial $x^n+y\in k[x,y]$ is irreducible over all fields, no? | |
| Jul 4, 2011 at 23:27 | comment | added | Mariano Suárez-Álvarez | Why do you think characteristic 2 is special in this regard? | |
| Jul 4, 2011 at 23:09 | history | asked | Bruno | CC BY-SA 3.0 |