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  "body": "\n## Summary\n\nLet $R$ be a [[ring|0894J980RK]] and let $I$ and $J$ be left [[ideals|0MYSA6MYNA]] of $R$.\nThe sum of $I$ and $J$ is $I + J = \\{a + b : a \\in I, b \\in J\\}$.\nIt is a left ideal, and it is the smallest left ideal that contains $I$ and $J$.\n\n## Remarks\n\nThe sum $I + J$ is the ideal [[generated by|030TZ0DQWT]] $I \\cup J$.\nIn $\\mathbb{Z}$, $m\\mathbb{Z} + n\\mathbb{Z} = d\\mathbb{Z}$, where $d$ is the greatest common divisor of $m$ and $n$.\nThe ideals $I$ and $J$ are [[coprime|0MDJP82TEH]] when $I + J = R$.\n\n## Explanations\n\n### L1 human\n\nTo add two ideals, take all the sums of one element from each.\nIn the integers, the sum of the multiples of $4$ and the multiples of $6$ is the set of the multiples of $2$.\n",
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