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  "body": "\n## Definition\n\nLet $L$ be a [[field|0QA8CHH8MG]].\nA subfield of $L$ is a [[subring|0859D58WPD]] $K \\subseteq L$ such that $a^{-1} \\in K$ for every nonzero $a \\in K$.\n\n## Remarks\n\nEquivalently, $K$ contains $0$ and $1$, and $K$ is closed under addition, negation, multiplication and the inverse of nonzero elements.\nA subfield is a field with the operations of $L$ restricted to $K$.\nThe rationals $\\mathbb{Q}$ are a subfield of $\\mathbb{R}$, and $\\mathbb{R}$ is a subfield of $\\mathbb{C}$.\nThe intersection of any family of subfields of $L$ is a subfield of $L$. The intersection of all of them is the [[prime subfield|0VPFBAY7MW]].\n\n## Explanations\n\n### L1 human\n\nA subfield is a smaller field that sits inside a bigger one.\nYou can add, subtract, multiply and divide its elements without leaving it.\nThe integers are a subring of $\\mathbb{Q}$, but not a subfield, because $1/2 \\notin \\mathbb{Z}$.\n",
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