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First of all, has the Koethe conjecture been solved ?! Does a proof of the following statement really imply the proof of the conjecture ?

  • The sum of two right nil ideals in any ring is nil.

Are there other equivalent statements that imply the conjecture ?

Thanks, SB

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Not solved. Many special cases though. The paper cited above looks nice, and another short survey is given in Lam's First Course in Noncommutative rings, around page 164. There are a bunch of equivalent statements there, but maybe the above paper covers them all.

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