Consider the ring $R= \mathbb Z [(1+\sqrt-19)/2]$. How do I prove it is not an euclidean domain?
Proving that the ring is not an euclidean domain
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$\begingroup$
abstract-algebra
ring-theory
1 Answers
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This is a fairly messy (at least as far as I know) proof. The most elementary proof I have seen can be found here
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1Here is a link to a file of the same name, I'm not sure it's the same one: http://www.maths.qmul.ac.uk/~raw/MTH5100/PIDnotED.pdf – 2016-06-04