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  "body": "\n## Definition\n\nA [[field extension|0WQ1A8SHTZ]] $L/K$ is simple if there is an element $\\theta \\in L$ with $L = K(\\theta)$.\nSuch an element $\\theta$ is a primitive element, or a generator, of $L/K$.\n\n## Remarks\n\nThe extensions $\\mathbb{C}/\\mathbb{R}$, generated by $i$, and $\\mathbb{Q}(\\sqrt{2})/\\mathbb{Q}$, generated by $\\sqrt{2}$, are simple.\nThe extension $\\mathbb{Q}(\\sqrt{3}, \\sqrt{7})/\\mathbb{Q}$ is simple, with the generator $\\sqrt{3} + \\sqrt{7}$.\nBy the [[primitive element theorem|0SVX98HYV1]], every finite separable extension is simple.\nFor finite fields, the term \"primitive element\" usually means a [[generator of the multiplicative group|0YAA9CJQXF]], which is a stronger condition.\n\n## Explanations\n\n### L1 human\n\nA simple extension is built by adding one new element to a field.\nSimple extensions are well understood: there is one kind for an algebraic generator and one kind for a transcendental generator.\n",
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