Every nonzero Boolean ring has characteristic 2

Prove that a nonzero Boolean ring has characteristic 2.


Let R be a Boolean ring. Note that 1+1 = (1+1)^2 = 1+1+1+1, so that 1+1 = 0. Thus the characteristic of R is at most 2. Since R is nontrivial, we have 1 \neq 0. Thus the characteristic of R is exactly 2.

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