Geodesic
A Generalization of Certain Rings of A. L. Foster
Canadian mathematical bulletin, Tome 6 (1963) no. 1, pp. 55-60

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The concept of a Boolean ring, as a ring A in which every element is idempotent (i. e., a2 = a for all a in A), was first introduced by Stone [4]. Boolean algebras and Boolean rings, though historically and conceptually different, were shown by Stone to be equationally interdefinable. Indeed, let (A, +, x) be a Boolean ring with unit 1, and let (A, ∪, ∩, ') be a Boolean algebra, where ∩, ∪, ', denote "union", " intersection", and "complement". The equations which convert the Boolean ring into a Boolean algebra are: I Conversely, the equations which convert the Boolean algebra into a Boolean ring are: II 
Yaqub, Adil. A Generalization of Certain Rings of A. L. Foster. Canadian mathematical bulletin, Tome 6 (1963) no. 1, pp. 55-60. doi: 10.4153/CMB-1963-008-4
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