Timeline for No canonical isomorphism
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 26, 2021 at 16:07 | comment | added | François Brunault | @LSpice Indeed, this quotient of $\mathbb{R}[\alpha_1,\alpha_2]$ is just one algebraic closure. There is no canonical isomorphism with the algebraic closure someone else may come up with, like $\mathbb{R}[x]/(x^2+1)$. | |
| Apr 26, 2021 at 15:18 | comment | added | LSpice | @FrançoisBrunault, what would it even mean to have a canonical isomorphism to a structure defined only up to isomorphism? | |
| Apr 24, 2021 at 10:53 | comment | added | François Brunault | @Oniqa One can define $\mathbb{C}$ as an algebraic closure of $\mathbb{R}$. It is unique only up to isomorphism. Explicitly one can take $\mathbb{R}[\alpha_1,\alpha_2]/(\alpha_1+\alpha_2,\alpha_1 \alpha_2 -1)$ and then $\{\alpha_1,\alpha_2\} = \{\pm i\}$. | |
| Apr 24, 2021 at 10:17 | comment | added | user178109 | What is your definition of $\mathbb{C}$? | |
| S Apr 24, 2021 at 0:50 | history | answered | Zach Teitler | CC BY-SA 4.0 | |
| S Apr 24, 2021 at 0:50 | history | made wiki | Post Made Community Wiki by Zach Teitler |