MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

share|cite|improve this question
This seems to be a nice survey: – Julian Kuelshammer Oct 17 '11 at 17:58
Thanks for the link ! As a matrix fan, I also found the following statement… 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

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.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.