Boolean ring

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Boolean ring

[¦bül·ē·ən ′riŋ]
(mathematics)
A commutative ring with the property that for every element a of the ring, a × a and a + a = 0; it can be shown to be equivalent to a Boolean algebra.
References in periodicals archive ?
Montgomery, A representation of generalized Boolean rings, Duke Math.
It follows that the proper subset A, a maximal set of B forms a Boolean ring.
Hence A is a maximal set with uni-element and by theorem 1 and definition A, a maximal set of B forms a Boolean ring.