
In mathematics, a Boolean ring R is a ring for which x2 = x for all x in R; that is, R consists only of idempotent elements. A Boolean ring is essentially the same thing as a Boolean algebra, with ring multiplication corresponding to conjunction or meet ∧, and ring addition to exclusive disjunction or symmetric difference (not disjunction ∨). ...
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http://en.wikipedia.org/wiki/Boolean_ring

a nonempty collection of sets having the properties that the union of two sets of the collection is a set in the collection and that the relative complement of each set with respect to any other set is in the collection. Cf. algebra of sets.
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https://www.infoplease.com/dictionary/boolean-ring
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