Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I'm looking for a reference of the following fact:

given a (countable?) amenable group $G$ and a (skew) field $K$, the following are equivalent:

(1) the group ring $K[G]$ is a domain;

(2) $K[G]$ is a (left and right) Ore domain.

I think to remember that this result is due to Beno Eckmann but, unfortunately, I cannot remember in which paper. I tried to look for this result and I'm not able to find it at the moment. Any reference would be strongly appreciated!

share|improve this question
    
I'll make the same question on mathoverflow as I did not receive any answer here. –  Simone May 24 '13 at 19:09
3  
This question has an answer on mathoverflow –  Julian Kuelshammer Jun 21 '13 at 20:36
    
@JulianKuelshammer: in view of the Crusade of Answers, could you suggest a way to post a formal answer to this question, please? –  Alexander Konovalov Jun 30 '13 at 8:40
    
I think that the best solution is a CW answer, when the answerer of the crosspost answer has not already duplicated their answer. If we spend too much time trying to get crosspost answererers to crosspost solutions, then I think we will spend too much time and energy, and secondly we might encourage some sort of rep-gaming that we don't want to develop. –  rschwieb Jul 29 '13 at 12:53
add comment

1 Answer

up vote 1 down vote accepted

This is a CW answer designed to get this question out of the unanswered queue.


Mark Sapir's answer to the crosspost of this question on MO was accepted. Here it is:

See here: Lück, Wolfgang, L2-invariants: theory and applications to geometry and K-theory. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], 44. Springer-Verlag, Berlin, 2002. xvi+595 pp., Example 8.16 on page 324.

share|improve this answer
add comment

Your Answer

 
discard

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.