Tell me more ×
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.
up vote 2 down vote favorite

Consider the ring $R= \mathbb Z [(1+\sqrt-19)/2]$. How do I prove it is not an euclidean domain?

share|improve this question

1 Answer

up vote 5 down vote accepted

This is a fairly messy (at least as far as I know) proof. The most elementary proof I have seen can be found here

share|improve this answer
1  
+1 I just spent the last 10 minutes reading the proof in the link. I really like this proof; there is clearly a conceptual idea of considering elements of small norm (which is important for our understanding of a Euclidean domain because the Euclidean algorithm tells us that elements of small norm have nice divisibility properties). Moreover, this conceptual idea is converted into a straightforward proof whose details only involve manipulations with complex numbers. – Amitesh Datta Nov 12 '11 at 10:05

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.