Timeline for Zero divisors in the boolean polynomial ring $\mathbb{F}_2[x_1,x_2,...,x_n]/(x_1^2-x_1,x_2^2-x_2,...x_n^2-x_n)$
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 25 at 6:49 | vote | accept | joro | ||
| Jan 18 at 17:25 | comment | added | Peter Taylor | Incidentally the "injective" and "such that their images are disjoint", which capture the original definition of $W$ as a "subset of $K$", are unused and unnecessary in this case. If $i \neq j$ then clearly $w(i) \neq w(j)$ and $w(i) \neq \overline{w}(j)$ since otherwise respectively $w(i) \overline{w}(j)$ or $w(i)w(j)$ would be zero, violating the condition. We can weaken to $w(i) \neq \overline{w}(i)$ (in the original formulation, $W[i] \neq W[i+k]$), but that constraint is then only relevant if there are non-zero square roots of zero in $K$. | |
| Jan 18 at 10:29 | comment | added | Peter Taylor | @joro, I don't understand the question, but it's possible that the edit I just completed already answers it. | |
| Jan 18 at 10:29 | history | edited | Peter Taylor | CC BY-SA 4.0 |
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| Jan 18 at 10:20 | comment | added | joro | Thanks. I suppose you can't verify candidate solution without enumerating the subsets, right? | |
| Jan 17 at 16:26 | history | answered | Peter Taylor | CC BY-SA 4.0 |