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.
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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. B is a Boolean-near-ring, whose proper subset is a Boolean-ring, then by definition, B is a SmarandacheBoolean-near-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.
On some characterization of Smarandache-boolean near-ring with sub-direct sum structure

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