Timeline for Extension field $\mathbb{C}(t,u)$ over $\mathbb{C}(t^n,u^n)$
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 10, 2016 at 13:03 | vote | accept | sunya hu | ||
| Sep 10, 2016 at 13:00 | answer | added | Alex Gavrilov | timeline score: 3 | |
| Sep 10, 2016 at 10:37 | comment | added | Alex Gavrilov | Yes, I was wrong there: there are some exceptions. I will better write an answer instead of a comment. | |
| Sep 10, 2016 at 8:38 | comment | added | sunya hu | $\mathbb{C}(t)$ is a proper subfield of $\mathbb{C}(t,u)$ since if $u \in \mathbb{C}(t)$ then $u = f(t)/g(t)$ where $f(x)$, $g(x)$ $ \in \mathbb{C}[x]$ but it yields $(f(t)/g(t))^2 + t^2 = 1$ since $t$ is transcendental hence it is impossible. $\mathbb{C}(t,u)$ is a splitting field over $\mathbb{C}(t)$ of a separable polynomial of $\mathbb{C}(t)[x]$ namely $x^2 + t^2 -1$ hence $\mathbb{C}(t,u)$ is Galois over $\mathbb{C}(t)$ | |
| Sep 10, 2016 at 6:48 | comment | added | sunya hu | the link is math.stackexchange.com/q/1920483/262757 | |
| Sep 10, 2016 at 6:33 | comment | added | YCor | please provide a link to the MathSE question | |
| Sep 10, 2016 at 6:32 | comment | added | Alex Gavrilov | What you did is basically a proof by contradiction that the extension you consider is not Galois. In fact, $\mathbb{C}(t,u)=\mathbb{C}(z)$, where $z=u+it$, and this field can't be a Galois extension of its subfield. | |
| Sep 10, 2016 at 1:19 | review | First posts | |||
| Sep 10, 2016 at 1:54 | |||||
| Sep 10, 2016 at 1:15 | history | asked | sunya hu | CC BY-SA 3.0 |