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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

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

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.

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