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  "body": "\n## Summary\n\nKurosh–Amitsur radical theory is the general theory of radicals of rings.\nA radical in this sense is a class of rings closed under homomorphic images.\nEvery ring must have a largest ideal in the class, and the quotient by that ideal must have no nonzero ideal in the class.\nThe [[Jacobson radical|XA0DCNH7WY]], the [[prime radical|WF117EJ2HF]], the [[Levitzki radical|9DD8M9R868]], the [[upper nilradical|3G2JQEYBEK]] and the [[Brown–McCoy radical|EWWP84BGSC]] are all examples.\nThe theory lets one prove facts about all these radicals at once, and it extends to other algebraic structures.\n\n## Explanations\n\n### L1 human\n\nMany constructions in ring theory pick out a \"bad part\" of a ring, an ideal one would like to remove.\nRemoving it should leave a ring with no bad part left.\nRadical theory turns this pattern into axioms.\nFor instance, the class of nil rings, the rings in which every element is nilpotent, is a radical class, and its radical is the largest nil ideal.\n",
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