In mathematics, a Boolean ring R is a ring for which x2 = x for all x in R, such as the ring of integers modulo 2. That is, R consists only of idempotent elements. Every Boolean ring gives rise to a Boolean algebra, with ring multiplication corresponding to conjunction or meet ∧, and ring addition to exclusive disjunction or symmetric difference (not disjunction ∨, which would constitute a semiring). Boolean rings are named after the founder of Boolean algebra, George Boole.
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