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A Boolean algebra is a commutative ring satisfying x²=x for every x, and sometimes required to have a unit; they have characteristic 2. For coding theory (notably dealing with subsets linear subspaces of spaces of Boolean functions), rather use the [coding-theory] or [linear-algebra] tag.
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Cardinality of the set of maximal ideals in a Boolean ring/algebra
I think this is false—is it supposed to be the other way around?
The Stone representation theorem embeds $B$ in $\prod_{\mathfrak{p} \in \operatorname{Spec} B} \mathbb{F}_2$, where $\operatorname{Spe …