Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. 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

Is $\mathbb{Z}[1/p]$ ($p\in \mathbb{N}$ prime) an euclidean domain?

I think that the answer is not, but i can't prove it.

I only can prove it is an unique factorization domain

share|cite|improve this question
Localization of a euclidean ring always gives a euclidean ring. – tfw cant into math Nov 1 '13 at 16:12
up vote 2 down vote accepted

Yes it is a Euclidean domain. As was noted in a comment, localization of a euclidean domain is euclidean. See here for more detailed answer by Pete L. Clark.

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.