Timeline for Is the minimal polynomial of an algebraic formal Laurent series always separable?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 25, 2022 at 11:13 | vote | accept | Jiu | ||
| Apr 23, 2022 at 12:54 | answer | added | reuns | timeline score: 4 | |
| Apr 23, 2022 at 12:45 | comment | added | Will Sawin | @reuns In view of the example $y^2 -x$, I thought we were considering separability mod $x$ (ignoring the claim that $y= \sqrt{x}$ is a double root, which suggests maybe instead we are working in characteristic $2$.) | |
| Apr 23, 2022 at 12:43 | comment | added | reuns | @WillSawin This cubic polynomial is separable, its discriminant is $-27x^2 - 4x\ne 0 $ | |
| Apr 22, 2022 at 23:49 | comment | added | Will Sawin | $y^2 (y-1) - x $ has a double root mod $x$ but also a single root. The single root lifts to an algebraic formal Laurent series by Hensel's lemma. Since $y^2 (y-1)-x$ is irreducible, its minimal polynomial has a double root. | |
| Apr 22, 2022 at 23:06 | history | asked | Jiu | CC BY-SA 4.0 |