Timeline for Classification of rings satisfying $a^4=a$
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 14, 2014 at 14:18 | comment | added | Martin Brandenburg | Meanwhile I have also found a proof for $X \cong G(F(X))$. | |
| Oct 14, 2014 at 6:53 | history | bounty ended | Martin Brandenburg | ||
| Oct 14, 2014 at 6:53 | vote | accept | Martin Brandenburg | ||
| Oct 13, 2014 at 14:19 | comment | added | Neil Strickland | I am happy for this to be made CW. | |
| Oct 13, 2014 at 11:22 | comment | added | Martin Brandenburg | I think I have found a proof that $R \to F(G(R))$ is an isomorphism, but it's quite long. Should I make this a CW answer? | |
| Oct 9, 2014 at 10:20 | comment | added | Martin Brandenburg | @EricWofsey: Yes, because then it is a closed subspace of $\prod_{r \in R} \mathbb{F}_4$. Notice that this is not a Zariski-like topology. | |
| Oct 9, 2014 at 10:17 | comment | added | Eric Wofsey | @MartinBrandenburg: It is a Stone space if you topologize it based on $\mathbb{F}_4$ being discrete, rather than only $\{0\}$ being closed. | |
| Oct 9, 2014 at 10:11 | comment | added | Martin Brandenburg | Unfortunately, $G(R)$ is not a Hausdorff space and not totally disconnected. For example, $G(\mathbb{F}_4)$ has two points and carries the indiscrete topology. Nevertheless, we can ask if $R \to \mathrm{Map}_{C_2}(\hom(R,\mathbb{F}_4),\mathbb{F}_4)$ is an isomorphism. It is injective, but I have no idea how to prove surjectivity. | |
| Oct 9, 2014 at 10:07 | history | edited | Martin Brandenburg | CC BY-SA 3.0 |
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| Sep 27, 2014 at 18:39 | comment | added | Martin Brandenburg | Hm, $\mathcal{X}$ is equivalent to the category of boolean rings with an action of $C_2$. Is there a direct algebraic way to see that this is $\mathcal{R}$? | |
| Sep 27, 2014 at 17:45 | history | answered | Neil Strickland | CC BY-SA 3.0 |