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  "body": "\n## Summary\n\nThe injective hull of a module $M$ is the smallest [[injective module|85H7PRHDPZ]] that contains $M$.\nEvery module has one, and it is unique up to an isomorphism that fixes $M$.\nInjective hulls are the building blocks of minimal injective resolutions.\nThe injective hull of the residue field of a local ring is the dualizing object of [[Matlis duality|2V9BR5XX6A]].\n\n## Explanations\n\n### L1 human\n\nAn injective module is one into which maps can always be extended.\nThe injective hull is the most economical way to enlarge $M$ into such a module.\nEvery nonzero piece of the hull touches $M$ itself, so nothing superfluous is added.\nFor example, the injective hull of the integers $\\Z$, as an abelian group, is the group of rational numbers $\\Q$.\n",
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