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  "body": "\n## Definition\n\nLet $R$ be a [[commutative ring|0GYGHKX834]] and let $a, b \\in R$.\nThe element $a$ divides $b$, written $a \\mid b$, if there is $c \\in R$ with $b = a c$.\nThen $a$ is a divisor of $b$, and $b$ is a multiple of $a$.\n\n## Remarks\n\nThe relation $a \\mid b$ holds if and only if $(b) \\subseteq (a)$ for the [[principal ideals|00A2EDFT9Q]].\nEvery element divides $0$, and $0$ divides only $0$.\nA [[unit|019NFGFPR5]] divides every element.\nIn $\\mathbb{Z}[i]$, $1 + i$ divides $2$, because $2 = (1 + i)(1 - i)$.\n\n## Explanations\n\n### L1 human\n\nDivisibility in a ring works as for integers: $a$ divides $b$ if $b$ is $a$ times some element of the ring.\nThe answer depends on the ring: $2$ does not divide $1$ in $\\mathbb{Z}$, but it does in $\\mathbb{Q}$.\n",
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