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

Every excellent ring is both universally catenary and Nagata. How "close" is a universally catenary Nagata ring to being excellent?

Context: I have not worked very much with the notions described above. While I certainly would not turn down a counterexample, I am more interested in getting an idea of how these notions are used in practice, and when it is appropriate to use one versus the other.

share|cite|improve this question
In this article by Christel Rotthaus, she constructs a three-dimensional regular local ring which is Nagata (universally Japanese) but not excellent. Perhaps it will give you some idea of how hard one must work for such examples. – Graham Leuschke Dec 2 '11 at 20:27
Unfortunately, I don't speak a word of German, but thanks for the reference in any case. – Charles Staats Dec 3 '11 at 2:10

Your Answer


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

Browse other questions tagged or ask your own question.