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  "body": "\n## Definition\n\nLet $R$ be a [[ring|0894J980RK]].\nFor a positive integer $n$, write $n \\cdot 1 = 1 + 1 + \\dots + 1$, with $n$ terms.\nIf there is a positive integer $n$ with $n \\cdot 1 = 0$ in $R$, then the characteristic of $R$ is the least such $n$.\nIf there is no such $n$, then the characteristic of $R$ is $0$.\n\n## Remarks\n\nThe rings $\\mathbb{Z}$, $\\mathbb{Q}$, $\\mathbb{R}$ and $\\mathbb{C}$ have characteristic $0$.\nFor $n \\ge 1$, the ring $\\mathbb{Z}/n\\mathbb{Z}$ has characteristic $n$.\nThe characteristic of $R$ is the nonnegative generator of the kernel of the unique ring homomorphism $\\mathbb{Z} \\to R$.\nThe [[characteristic of an integral domain is zero or prime|00758QM6JJ]].\n\n## Explanations\n\n### L1 human\n\nStart with $1$ and keep adding $1$.\nIn the integers you never come back to $0$, so the characteristic is $0$.\nModulo $5$, you get $0$ after five steps, so the characteristic is $5$.\n",
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