query: $k[x,y]_{2\bullet}\cong k[z_0,z_1,z_2]/(z_2z_0-z_1^2)$
positive_passages.docid: 149973
positive_passages.text: Showing the following coordinate rings are not isomorphic
negative_passages.docid: 129732
negative_passages.text: What is $\operatorname{Aut}(\mathbb{Z}_2\oplus \mathbb{Z}_2)$?
negative_passages.docid: 109596
negative_passages.text: Isomorphism from $\mathrm{Aut}(\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z})$ to $S_3$
negative_passages.docid: 133915
negative_passages.text: In which case $M_1 \times N \cong M_2 \times N \Rightarrow M_1 \cong M_2$ is true?
negative_passages.docid: 8602
negative_passages.text: Galois Group of $(x^2-p_1)\cdots(x^2-p_n)$
negative_passages.docid: 134840
negative_passages.text: Generators and relations for $\text{PSL}(2, \mathbb{F}_q)$
negative_passages.docid: 46211
negative_passages.text: $(K[x,y,z]/(x^2+y^3+z^7))_{(x,y,z)}$ is a UFD.
negative_passages.docid: 154837
negative_passages.text: mapping properties of $(1−z)^i$
negative_passages.docid: 8374
negative_passages.text: How to prove that $R/I \otimes_R M \cong M / IM$
negative_passages.docid: 128711
negative_passages.text: $(\Bbb Z\oplus \Bbb Z)[X] \not\cong \Bbb Z[X]\oplus \Bbb Z[X]\,$?
negative_passages.docid: 14895
negative_passages.text: Reference for the subgroup structure of $\rm{PSL}_2(q)$
negative_passages.docid: 3203
negative_passages.text: Quotient group $\mathbb Z^n/\ \text{im}(A)$
negative_passages.docid: 51898
negative_passages.text: Show that $\operatorname{Hom}_{R} (R,M) \cong M$
negative_passages.docid: 133238
negative_passages.text: Why does $\mathrm{Tor}_0^R(M,N)\cong M\otimes_R N$?
negative_passages.docid: 53266
negative_passages.text: Show that $R/I\otimes_R R/J\cong R/(I+J)$
negative_passages.docid: 35626
negative_passages.text: Is $(\mathbb{R}^2, lexicographic) \cong (\mathbb{R}, discrete)\times (\mathbb{R}, usual)$?
negative_passages.docid: 63104
negative_passages.text: Dual cone of $K = \{(x,t) \mid \| \boldsymbol{x} \|_1 \le t \}$