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  "body": "\n## Definition\n\nLet $K$ and $L$ be [[fields|0QA8CHH8MG]].\nThe field $L$ is an extension of $K$ if $K$ is a [[subfield|07QY5RPFBR]] of $L$.\nOne writes $L/K$ for this field extension.\n\n## Remarks\n\nOften one also calls $L$ an extension of $K$ when there is an injective [[ring homomorphism|0GGE0Z0JQ1]] $K \\to L$. Then one identifies $K$ with its image.\nAn extension $L/K$ makes $L$ a vector space over $K$. Its dimension is the [[degree of the extension|0GS74FGFEK]].\nExamples: $\\mathbb{C}/\\mathbb{R}$, $\\mathbb{R}/\\mathbb{Q}$ and $\\mathbb{Q}(\\sqrt{2})/\\mathbb{Q}$.\nThe notation $L/K$ does not mean a quotient.\n\n## Explanations\n\n### L1 human\n\nA field extension is a bigger field that contains a given field.\nFor example, the complex numbers extend the real numbers by an element $i$ with $i^2 = -1$.\nField theory studies how the bigger field is built from the smaller one.\n",
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