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
2026-03-28 06:48:08.1774680488
Is $\mathbb{Z}[1/p]$ an euclidean domain?
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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.