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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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This seems to be a nice survey: math.bas.bg/serdica/2001/2001-159-170.pdf –  Julian Kuelshammer Oct 17 '11 at 17:58
    
Thanks for the link ! As a matrix fan, I also found the following statement books.google.co.uk/… interesting : - If $I$ is a nil ideal in $R$ then $M_n( I)$ is a nil ideal in $M_n(R)$ ! –  Serifo Blade Oct 17 '11 at 23:10
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I'd never yet met a matrix fan :) –  Mariano Suárez-Alvarez Dec 18 '11 at 1:37
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Oh yes I am a big fan of matrix rings !:) –  Serifo Blade Dec 18 '11 at 17:21

1 Answer 1

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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