Timeline for On Galois' criterion for resolvents
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 5, 2020 at 17:31 | review | Close votes | |||
| Aug 6, 2020 at 19:16 | |||||
| Aug 5, 2020 at 17:13 | comment | added | Pace Nielsen | Let $K=L=\mathbb{Q}$ and take $f(x)=x(x-1)$. Thus, the two roots can be ordered as $x_1=0,x_2=1$. Any polynomial $Q(X_1,X_2)$ will yield a primitive element for this extension when we evaluate at $x_1,x_2$. | |
| Aug 5, 2020 at 13:14 | comment | added | Pace Nielsen | (C1) is only necessary for a primitive element when $n!$ is the degree of the extension $L/K$. But there are examples of degree $3$ Galois extensions, and $n!$ never equals $3$. | |
| Aug 5, 2020 at 5:25 | history | edited | MathCrawler | CC BY-SA 4.0 |
edited body
|
| Aug 4, 2020 at 20:00 | comment | added | Abdelmalek Abdesselam | Hopefully useful reference on non-modern Galois Theory, arxiv.org/abs/1301.7116 | |
| Aug 4, 2020 at 15:36 | comment | added | LSpice | Also, since you edited it back in you obviously want it, so I apologise for an edit that went against your intentions; but "a bunch of at most $n!$ different values" is not usual English. Usually one would say something like "a bunch of different values, at most $n!$" or just "at most $n!$ different values". | |
| Aug 4, 2020 at 13:00 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title, added tag
|
| Aug 4, 2020 at 12:55 | history | edited | MathCrawler | CC BY-SA 4.0 |
edited body
|
| Aug 4, 2020 at 1:18 | history | edited | LSpice | CC BY-SA 4.0 |
Various proofreading
|
| Aug 4, 2020 at 1:15 | comment | added | LSpice | Despite your definition, I don't know what "generic" means. Which relation is "a certain nontrivial polynomial relation"? What does it mean to speak of whether a polynomial (which is what you are calling generic) satisfies a polynomial relation? | |
| Aug 4, 2020 at 0:34 | history | asked | MathCrawler | CC BY-SA 4.0 |