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  "body": "\n## Summary\n\nThe Levitzki radical of a ring is its largest locally nilpotent ideal.\nAn ideal is locally nilpotent when every finite subset of it generates a nilpotent subring.\nIt lies between the [[prime radical|WF117EJ2HF]] and the [[upper nilradical|3G2JQEYBEK]].\nIt is one of the classical radicals of the [[Kurosh–Amitsur radical theory|A72J7ZVNR5]].\n\n## Explanations\n\n### L1 human\n\nA nilpotent ideal is one where any long enough product of its elements is zero.\nA locally nilpotent ideal asks less: only products of elements chosen from a fixed finite set must vanish when they are long enough.\nThe Levitzki radical collects all such ideals.\nIn a commutative ring every nilpotent element generates a nilpotent ideal, and the Levitzki radical is the set of nilpotent elements.\n",
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