query: Is $\mathbb{Z}[\sqrt{-7}]$ a UFD or not?
positive_passages.docid: 24413
positive_passages.text: Why is $\mathbb{Z}[\sqrt{-n}], n\ge 3$ not a UFD?
negative_passages.docid: 97258
negative_passages.text: Give $\ker(\phi)$ for $\phi: \mathbb{Z} \to \mathbb{Z_7}$ such that $\phi(1)=4$
negative_passages.docid: 61987
negative_passages.text: $x^2+1=0$ in $\mathbb{Z}_7$
negative_passages.docid: 135152
negative_passages.text: Non-UFD integral domain such that prime is equivalent to irreducible?
negative_passages.docid: 1020
negative_passages.text: Proving that $\mathbb{Z}[\sqrt{2}]$ is a Euclidean domain
negative_passages.docid: 99423
negative_passages.text: Is it true every ideal of $\mathbb{Z}[x]$ is finitely generated?
negative_passages.docid: 55050
negative_passages.text: How to show that $\mathbb{Q}(i,\sqrt[4]{1+i} )$ is not contained in any cyclotomic extension of $\mathbb{Q}(i)$?
negative_passages.docid: 112556
negative_passages.text: When is $F(\sqrt c)$ a field?
negative_passages.docid: 135524
negative_passages.text: Is $\mathrm{ZFC}^E$ outright inconsistent?
negative_passages.docid: 83798
negative_passages.text: Does $A$ a UFD imply that  $A[T]$ is also a UFD?
negative_passages.docid: 19230
negative_passages.text: Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
negative_passages.docid: 6171
negative_passages.text: Isomorphism between $\Bbb{Z}[\sqrt{d}]$ and a quotient of $\Bbb{Z}[X].$
negative_passages.docid: 4105
negative_passages.text: Irreducible but not prime in $\mathbb{Z}[\sqrt{-5}] $
negative_passages.docid: 129521
negative_passages.text: Is $\sqrt[3]{5}$ in $\mathbb Q(\sqrt[3]{2})$?
negative_passages.docid: 6837
negative_passages.text: How to quotient $\mathbb Z [\sqrt{-11}] / (1+\sqrt{-11})$?
negative_passages.docid: 57101
negative_passages.text: About the localization of a UFD
negative_passages.docid: 35691
negative_passages.text: $\mathbb Z[\sqrt 3]$ contains infinitely many units