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  "body": "\n## Statement\n\nLet $R$ be an [[integral domain|09S3PFBEPM]].\nThen the [[characteristic|0P7CH1CND5]] of $R$ is $0$ or a prime number.\n\n## Remarks\n\nThe proof: suppose that the characteristic is $n = a b$ with $1 \u003c a, b \u003c n$. Then $(a \\cdot 1)(b \\cdot 1) = n \\cdot 1 = 0$, but $a \\cdot 1 \\neq 0$ and $b \\cdot 1 \\neq 0$.\nThe characteristic is not $1$, because $1 \\neq 0$ in an integral domain.\nIn particular, the characteristic of a [[field|0QA8CHH8MG]] is $0$ or a prime number.\nThe ring $\\mathbb{Z}/6\\mathbb{Z}$ has characteristic $6$, and it is not an integral domain.\n\n## Explanations\n\n### L1 human\n\nIf $6 \\cdot 1 = 0$ in a ring, then $(2 \\cdot 1)(3 \\cdot 1) = 0$.\nIn an integral domain, this forces $2 \\cdot 1 = 0$ or $3 \\cdot 1 = 0$.\nSo the least $n$ with $n \\cdot 1 = 0$ cannot be a product of two smaller numbers.\n",
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