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  "body": "\n## Definition\n\nA Boolean ring is a ring $R$ with identity such that $x^2 = x$ for every $x \\in R$.\n\n## Remarks\n\nIn a Boolean ring, $x + x = 0$ for every $x$, and the ring is commutative.\nThe ring $\\mathbb{Z}/2\\mathbb{Z}$ is a Boolean ring. The power set of a set is a Boolean ring, with symmetric difference as addition and intersection as multiplication.\nEach Boolean ring is a [[Boolean algebra|06GKBTAA5E]] with $x \\wedge y = xy$, $x \\vee y = x + y + xy$ and $\\neg x = 1 + x$. This gives a correspondence between Boolean rings and Boolean algebras.\n\n## Explanations\n\n### L1 human\n\nA Boolean ring is a ring in which squaring changes nothing.\nIt is the same thing as a Boolean algebra, written with plus and times instead of or and and.\n",
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