Is there any field other than $\mathbb{F}_2$ which has $1+1=0$ ? My initial feeling was no but I don't know how to prove it. Can someone help ?
2026-03-27 01:43:21.1774575801
A field with $2=0$
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This property is called "characteristic $2$", and many fields have it. $\Bbb F_2$ is in some sense the most "basic" one, but we also have examples like $$ \Bbb F_4=\Bbb F_2[t]/(t^2+t+1) $$ or $\Bbb F_2(x)$, the field of rational functions in one variable with coefficients from $\Bbb F_2$.