# Is $\mathbb{Z}[1/p]$ an euclidean domain?

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

-
Localization of a euclidean ring always gives a euclidean ring. – tfw cant into math Nov 1 '13 at 16:12