query: Show that $\Bbb C[x,y]/I$ is not isomorphic to $\Bbb C[z]$
positive_passages.docid: 155604
positive_passages.text: Show that $k[x,y]/(xy-1)$ is not isomorphic to a polynomial ring in one variable.
negative_passages.docid: 158502
negative_passages.text: Showing $\sin(\bar{z})$ is not analytic at any point of $\mathbb{C}$
negative_passages.docid: 1720
negative_passages.text: Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
negative_passages.docid: 88474
negative_passages.text: $\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
negative_passages.docid: 47914
negative_passages.text: Prove $\Bbb{Z}_{100} \times \Bbb{Z}_{10}$ is not isomorphic to $\Bbb{Z}_{1000}$
negative_passages.docid: 144572
negative_passages.text: Proof that ideals in $C[0,1]$ are of the form $M_c$ that should not involve Zorn's Lemma
negative_passages.docid: 94747
negative_passages.text: Show that the rings $2\mathbb{Z}$ and $3\mathbb{Z}$ are not isomorphic.
negative_passages.docid: 137285
negative_passages.text: Prove $\mathbb{Z}_2 \times \mathbb{Z}_2$ is not isomorphic to $\mathbb{Z}_4$
negative_passages.docid: 66169
negative_passages.text: Ring of order $n$ is isomorphic to $\Bbb Z/n\Bbb Z$, with $n$ square-free
negative_passages.docid: 6171
negative_passages.text: Isomorphism between $\Bbb{Z}[\sqrt{d}]$ and a quotient of $\Bbb{Z}[X].$
negative_passages.docid: 18484
negative_passages.text: Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
negative_passages.docid: 62635
negative_passages.text: Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.
negative_passages.docid: 95764
negative_passages.text: Prove that the additive groups $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic.
negative_passages.docid: 126927
negative_passages.text: $\mathbb Q$ is not the direct product of two non-trivial groups.
negative_passages.docid: 77735
negative_passages.text: When $\Bbb Z_n$ is a domain. Counterexample to $ab \equiv 0 \Rightarrow a\equiv 0$ or $b\equiv 0\pmod n$
negative_passages.docid: 40321
negative_passages.text: $\operatorname{Aut}(\mathbb Z_n)$ is isomorphic to $U_n$.
negative_passages.docid: 1686
negative_passages.text: Show that quotient rings are not isomorphic