query: Prove $S^{-1}A \cong A[x]/(bX-1)$
positive_passages.docid: 29359
positive_passages.text: Localisation isomorphic to a quotient of polynomial ring
negative_passages.docid: 18330
negative_passages.text: Does $R[x] \cong S[x]$ imply $R \cong S$?
negative_passages.docid: 118299
negative_passages.text: Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$
negative_passages.docid: 26741
negative_passages.text: How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
negative_passages.docid: 122741
negative_passages.text: $x^2$ is congruent to $-1 \bmod p$
negative_passages.docid: 112080
negative_passages.text: Proving the Product Rule for exponents with the same base
negative_passages.docid: 139011
negative_passages.text: How to prove $B-A \succeq 0 \Leftrightarrow$ ellipsoid $x^TBx \leq 1$ contains $x^TAx \leq 1$?
negative_passages.docid: 117688
negative_passages.text: Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$
negative_passages.docid: 7903
negative_passages.text: Prove that $B[x] \cap B[x^{-1}]$ is integral over $B$
negative_passages.docid: 77969
negative_passages.text: Question about proof for $S_4 \cong V_4 \rtimes S_3$
negative_passages.docid: 5526
negative_passages.text: Prove that $ℤ[i]^*= \{1,-1,i,-i\}$
negative_passages.docid: 21553
negative_passages.text: Prove that $\nabla_{\mathrm X} \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) = - \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}$
negative_passages.docid: 29231
negative_passages.text: Proof of : $x^{n}\equiv x^{\varphi(m)+[n \bmod \varphi(m)]} \mod m$
negative_passages.docid: 98855
negative_passages.text: Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
negative_passages.docid: 78263
negative_passages.text: Prove $GL_n(\Bbb{R})/SL_n(\Bbb{R}) \cong \Bbb{R}^\times$
negative_passages.docid: 27281
negative_passages.text: How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
negative_passages.docid: 147564
negative_passages.text: Why does $(A/I)\otimes_R (B/J)\cong(A\otimes_R B)/(I\otimes_R 1+1\otimes_R J)$?