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  "body": "\n## Summary\n\nThe socle of a module is the sum of all its [[simple submodules|G00C22AEDH]].\nIt is the largest [[semisimple submodule|N3MRHDKDGC]] of the module.\nIt measures the part of a module that is built directly from simple pieces.\nIt is a basic tool in the study of Artinian rings and injective modules.\n\n## Explanations\n\n### L1 human\n\nSimple modules are the atoms of module theory: they have no proper nonzero submodules.\nThe socle collects every atom that sits at the bottom of a module.\nPicture a module as a building: the socle is its ground floor.\nFor example, in the $\\Z$-module $\\Z/12\\Z$ the simple submodules are $\\set{0, 6}$ and $\\set{0, 4, 8}$, and their sum is the socle, the subgroup generated by $2$, which has $6$ elements.\n",
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