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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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    $\begingroup$ This seems to be a nice survey: math.bas.bg/serdica/2001/2001-159-170.pdf $\endgroup$
    – Julian Kuelshammer
    Commented Oct 17, 2011 at 17:58
  • $\begingroup$ 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 $M_n(R)$ ! $\endgroup$
    – Serifo Blade
    Commented Oct 17, 2011 at 23:10
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    $\begingroup$ I'd never yet met a matrix fan :) $\endgroup$
    – Mariano Suárez-Álvarez
    Commented Dec 18, 2011 at 1:37
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    $\begingroup$ Oh yes I am a big fan of matrix rings !:) $\endgroup$
    – Serifo Blade
    Commented Dec 18, 2011 at 17:21

1 Answer 1

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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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