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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

flag	asked Oct 17 2011 at 17:46 Serifo Blade 51●1

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This seems to be a nice survey: math.bas.bg/serdica/2001/2001-159-170.pdf – Julian Kuelshammer Oct 17 2011 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 2011 at 23:10

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I'd never yet met a matrix fan :) – Mariano Suárez-Alvarez Dec 18 2011 at 1:37

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Oh yes I am a big fan of matrix rings !:) – Serifo Blade Dec 18 2011 at 17:21

rschwieb · Answer 1 · 2011-12-18 01:33:17Z UTC

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.

Koethe conjecture

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