query: $K[x,y]/\langle x^2-y^3\rangle \cong K[t^2,t^3]$
positive_passages.docid: 23099
positive_passages.text: Verifying that the ideal $(x^3-y^2)$ is prime
negative_passages.docid: 134840
negative_passages.text: Generators and relations for $\text{PSL}(2, \mathbb{F}_q)$
negative_passages.docid: 85752
negative_passages.text: Show that $M=\frac{\mathbb{Z}^3}{\langle (3,3,1),(2,2,2)\rangle}$ is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}_4$ as $\mathbb{Z}$-modules
negative_passages.docid: 63478
negative_passages.text: Is $\mathbb{Q}(\sqrt{2}) \cong \mathbb{Q}(\sqrt{3})$?
negative_passages.docid: 36137
negative_passages.text: Prove $GL_2(\mathbb{Z}/2\mathbb{Z})$ is isomorphic to $S_3$
negative_passages.docid: 88199
negative_passages.text: The commutator subgroup of a quotient in terms of the commutator subgroup and the kernel
negative_passages.docid: 102871
negative_passages.text: $\langle r\rangle$ maximal $\iff r$ irreducible
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: 27086
negative_passages.text: proof for $\langle q| p \rangle = e^{ipq}$
negative_passages.docid: 115876
negative_passages.text: $D_6 \cong D_3\times \mathbb Z_2$
negative_passages.docid: 23037
negative_passages.text: Computing the order of $\mathrm{SL}_2(\mathbb F_p)$ as the kernel of $\mathrm{GL}_2(\mathbb F_p)$
negative_passages.docid: 94296
negative_passages.text: Classifying the factor group $(\mathbb{Z} \times \mathbb{Z})/\langle (2, 2) \rangle$
negative_passages.docid: 111248
negative_passages.text: The Uniqueness of a Coset of $R[x]/\langle f\rangle$ where $f$ is a Polynomial of Degree $d$ in $R[x]$
negative_passages.docid: 29359
negative_passages.text: Localisation isomorphic to a quotient of polynomial ring
negative_passages.docid: 31919
negative_passages.text: What can we say about the inner product $\langle f(t),f'(t) \rangle$?
negative_passages.docid: 65873
negative_passages.text: A proof for Atiyah-Macdonald Exercise I.21.iii
negative_passages.docid: 128985
negative_passages.text: Show that $\langle x,y\rangle_A = \langle Ax,Ay\rangle$ is an inner product on $\mathbb R^n$