query: $X=Z(xy-1)\subset \mathbb{A}_k^2$ is not isomorphic to $\mathbb{A}^1_k$
positive_passages.docid: 156679
positive_passages.text: $K[X,Y]/(XY-1)$ not isomorphic to $K[T]$
negative_passages.docid: 62635
negative_passages.text: Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.
negative_passages.docid: 33370
negative_passages.text: Show that the one point compactification of $\mathbb{Q}$ is not Hausdorff
negative_passages.docid: 85586
negative_passages.text: Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
negative_passages.docid: 133636
negative_passages.text: Is $\mathbb Z[X]/(X^2-1)$ a domain?
negative_passages.docid: 95764
negative_passages.text: Prove that the additive groups $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic.
negative_passages.docid: 75970
negative_passages.text: $\mathbb Z[1/2]$ is not finitely generated?
negative_passages.docid: 156457
negative_passages.text: Show that $K[x,xy,xy^2,\dots]$ is not Noetherian
negative_passages.docid: 128732
negative_passages.text: $\mathbb Z_{p^n}$ is not the direct product of any family of its proper subgroups
negative_passages.docid: 9794
negative_passages.text: Quotient ring of Gaussian integers $\mathbb{Z}[i]/(a+bi)$ when $a$ and $b$ are NOT coprime
negative_passages.docid: 104562
negative_passages.text: Prove that $\mathbb{Z}$ is not isomorphic to additive group of any vector space over any field.
negative_passages.docid: 122012
negative_passages.text: The ideal $(x,y)$ is not a free $K[x,y]$-module
negative_passages.docid: 39114
negative_passages.text: Prove that a set in $\mathbb R^3$ is not an algebraic set
negative_passages.docid: 74330
negative_passages.text: $\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
negative_passages.docid: 25050
negative_passages.text: To prove that $(F,+)$ and $(F-\{0\},\cdot)$ are not isomorphic as groups.
negative_passages.docid: 45627
negative_passages.text: Find a sub-ring of M(2, $\mathbb{Q}$) which is isomorphic to $\mathbb{Q}$
negative_passages.docid: 157915
negative_passages.text: Isomorphism between the group $(\mathbb Z[x], +)$ and $(\mathbb Q_{>0}, .)$