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About: Kurosh problem     Goto   Sponge   NotDistinct   Permalink

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In mathematics, the Kurosh problem is one general problem, and several more special questions, in ring theory. The general problem is known to have a negative solution, since one of the special cases has been shown to have counterexamples. These matters were brought up by Aleksandr Gennadievich Kurosh as analogues of the Burnside problem in group theory. Golod showed a counterexample to that case, as an application of the Golod–Shafarevich theorem. The Kurosh problem on group algebras concerns the augmentation ideal I. If I is a nil ideal, is the group algebra locally nilpotent?