Timeline for Does "tensoring" with a fixed field preserve Galois extensions of finite fields?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 29, 2020 at 14:42 | comment | added | Zoorado | Your argument seems to not require any assumption of finiteness of the fields or of the extension. Is that correct? | |
| Apr 29, 2020 at 12:17 | comment | added | abx | Yes. The action of the Galois group $G$ on $L$ extends to an action on $K\otimes _{\mathbb{F}_p}L$, and since the functor $K\otimes _{\mathbb{F}_p}-$ is exact, the $G$-invariant subfield is $K\otimes_{\mathbb{F}_p}\mathbb{F}_p=K$. Thus $(K\otimes_{\mathbb{F}_p}L)/K$ is Galois with group $G$. | |
| Apr 29, 2020 at 10:39 | history | edited | Zoorado | CC BY-SA 4.0 |
Added the assumption that the tensor product is a field
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| Apr 29, 2020 at 10:37 | comment | added | Zoorado | Yes you are right. Let me make an edit. | |
| Apr 29, 2020 at 9:51 | comment | added | Dmitry Vaintrob | The tensor product of two fields will not in general be a field. | |
| Apr 29, 2020 at 9:48 | history | asked | Zoorado | CC BY-SA 4.0 |