# Koethe conjecture

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
I'd never yet met a matrix fan :) –  Mariano Suárez-Alvarez Dec 18 '11 at 1:37
Oh yes I am a big fan of matrix rings !:) –  Serifo Blade Dec 18 '11 at 17:21