Timeline for Extensions of fields with lots of symmetry
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 26, 2010 at 16:52 | comment | added | Mariano Suárez-Álvarez | Ah. I'd missed the fact that $k$ is algebraically closed. Thanks! | |
| Feb 26, 2010 at 15:25 | comment | added | Georges Elencwajg | Take any x in E but not in k. Then x is transcendental over k, because k is algebraically closed. Since K has transcendence degree 1 over k, the singleton {x} is a transcendence basis of K over k and so K is algebraic over k(x), and a fortiori K is algebraic over E. | |
| Feb 26, 2010 at 15:13 | comment | added | Mariano Suárez-Álvarez | Why is $K$ algebraic over $E$? | |
| Feb 26, 2010 at 15:07 | history | answered | Georges Elencwajg | CC BY-SA 2.5 |