$\mathbb{Z}[\frac{1-\sqrt{-19}}{2}]$ - principal ring, but not an euclidean ring

Asked Apr 29 '16 at 02:01

Active Apr 29 '16 at 02:01

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I am stucked on the problem. Is there someone who could tell me why $\mathbb{Z}[\frac{1-\sqrt{-19}}{2}]$ is a principal ring, but it is not an euclidean ring?

asked Apr 29 '16 at 02:01

http://math.stackexchange.com/q/857971/9464 – Apr 29 '16 at 02:08
http://www.math.ubc.ca/~reichst/423-project-pid-not-euclidean-siqi-wei.pdf – Apr 29 '16 at 02:09
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http://math.stackexchange.com/q/998716/9464 – Apr 29 '16 at 02:17

$\mathbb{Z}[\frac{1-\sqrt{-19}}{2}]$ - principal ring, but not an euclidean ring

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