Boolean ring

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In mathematics, a Boolean ring is a ring for which for all in, 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, and ring addition to exclusive disjunction or symmetric difference (not disjunction, 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.

Source: https://en.wikipedia.org/wiki/Boolean_ring
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