Boolean ring

In mathematics, a Boolean ring $R$ is a ring for which $x 2 = x$ for all $x$ in $R$ , that is, a ring that consists of only idempotent elements. An example is the ring of integers modulo 2.

Every Boolean ring gives rise to a Boolean algebra, with ring multiplication corresponding to conjunction or meet $\land$ , and ring addition to exclusive disjunction or symmetric difference (not disjunction $\lor$ , which would constitute a semiring). Conversely, every Boolean algebra gives rise to a Boolean ring. Boolean rings are named after the founder of Boolean algebra, George Boole.

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