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  "body": "\n## Definition\n\nLet $K$ be a [[field|0QA8CHH8MG]].\nThe prime subfield of $K$ is the intersection of all the [[subfields|07QY5RPFBR]] of $K$.\nIt is the smallest subfield of $K$.\n\n## Remarks\n\nIf the [[characteristic|0P7CH1CND5]] of $K$ is a prime $p$, then the prime subfield is isomorphic to $\\mathbb{F}_p = \\mathbb{Z}/p\\mathbb{Z}$.\nIf the characteristic of $K$ is $0$, then the prime subfield is isomorphic to $\\mathbb{Q}$.\nThe prime subfield of $\\mathbb{R}$ is $\\mathbb{Q}$.\n\n## Explanations\n\n### L1 human\n\nEvery subfield contains $0$ and $1$, and so it contains all the sums $1 + 1 + \\dots + 1$ and their quotients.\nThese elements form the prime subfield.\nIn the real numbers, they are exactly the rational numbers.\n",
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