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  "body": "\n## Summary\n\nAn Artinian module is a module in which every decreasing chain of submodules stops after finitely many steps.\nIt is the condition dual to that of a [[Noetherian module|AK1ZRCXR32]].\nA module is both Artinian and Noetherian exactly when it has finite [[length|CZSCNZH8VY]].\n\n## Explanations\n\n### L1 human\n\nIn an Artinian module you cannot keep shrinking submodules forever.\nA finite abelian group, seen as a $\\Z$-module, is Artinian, since it has only finitely many subgroups.\nThe group $\\Z$ is not Artinian, because $2\\Z \\supset 4\\Z \\supset 8\\Z \\supset \\cdots$ never stops.\nThe two chain conditions are different: the group of all complex roots of unity of order a power of a prime $p$ is Artinian but not Noetherian as a $\\Z$-module.\n",
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