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  "body": "\n## Definition\n\nAn integral domain is a [[commutative ring|0GYGHKX834]] $R$ with these two properties.\n\n1. $1 \\neq 0$ in $R$.\n2. For all $a, b \\in R$, if $a b = 0$, then $a = 0$ or $b = 0$.\n\nEquivalently, $R$ is a nonzero commutative ring in which $0$ is the only [[zero divisor|0K26YKNBSA]].\n\n## Remarks\n\nThe integers $\\mathbb{Z}$ and every [[field|0QA8CHH8MG]] are integral domains.\nThe ring $\\mathbb{Z}/6\\mathbb{Z}$ is not an integral domain, because $2 \\cdot 3 = 0$.\nIn an integral domain, [[cancellation|0GJM24EXP9]] holds for nonzero factors.\nSome authors, and Mathlib, also use the word domain for a noncommutative ring with property 2.\n\n## Explanations\n\n### L1 human\n\nAn integral domain is a ring that behaves like the integers for products.\nIf a product is zero, then one of the factors is zero.\nThis is what you use when you solve $(x - 2)(x - 3) = 0$.\n",
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