query: Is $\mathbb Z [(1+\sqrt{-19})/2]$ an Euclidean domain?
positive_passages.docid: 24351
positive_passages.text: The ring $\Bbb Z\left [\frac{-1+\sqrt{-19}}{2}\right ]$ is not a Euclidean domain
negative_passages.docid: 138944
negative_passages.text: Is $\mathbb Z[\sqrt{-3}]$ Euclidean under some other norm?
negative_passages.docid: 53331
negative_passages.text: $\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$
negative_passages.docid: 110726
negative_passages.text: Example of a non-gcd domain
negative_passages.docid: 95863
negative_passages.text: Describe the units in $\mathbb{Z}[\sqrt{-d}]$
negative_passages.docid: 92211
negative_passages.text: When are $\mathbb Z_m$ and $\mathbb Z_n$ homomorphic?
negative_passages.docid: 19884
negative_passages.text: The units of $\mathbb Z_4[x]$
negative_passages.docid: 66238
negative_passages.text: Proving $\mathbb{Z}[\sqrt {10}]$ is not a UFD
negative_passages.docid: 138256
negative_passages.text: What's the difference between $\mathbb{Q}[\sqrt{-d}]$ and $\mathbb{Q}(\sqrt{-d})$?
negative_passages.docid: 46047
negative_passages.text: Check whether the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$ is a field or an integral domain
negative_passages.docid: 41872
negative_passages.text: Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$
negative_passages.docid: 86015
negative_passages.text: $\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
negative_passages.docid: 48162
negative_passages.text: Is the subset $[0, \sqrt2] ∩\mathbb{Q} ⊂ \mathbb{Q}$ closed, bounded, compact?
negative_passages.docid: 121845
negative_passages.text: Quotient of polynomials, PID but not Euclidean domain?
negative_passages.docid: 5893
negative_passages.text: On the commutative property of multiplication (domain of integers, possibly reals)
negative_passages.docid: 18887
negative_passages.text: Euclidean domain in which the quotient and remainder are always unique
negative_passages.docid: 55900
negative_passages.text: Is there a ring homomorphism $M_2(\mathbb Z)\to \mathbb Z$?