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  "body": "\n## Definition\n\nLet $R$ be a [[commutative ring|0GYGHKX834]] and let $a, b \\in R$.\nThe elements $a$ and $b$ are associates, written $a \\sim b$, if there is a [[unit|019NFGFPR5]] $u \\in R$ with $b = u a$.\n\n## Remarks\n\nBeing associates is an equivalence relation.\nIn an [[integral domain|09S3PFBEPM]], $a \\sim b$ if and only if $a \\mid b$ and $b \\mid a$, if and only if $(a) = (b)$.\nIn $\\mathbb{Z}$, the associates of $n$ are $n$ and $-n$.\nIn $\\mathbb{Z}[i]$, the associates of $1 + i$ are $1 + i$, $-1 - i$, $-1 + i$ and $1 - i$.\n\n## Explanations\n\n### L1 human\n\nAssociates are elements that differ only by a unit factor.\nFor divisibility they behave in the same way.\nIn the integers, $6$ and $-6$ are associates.\n",
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