query: $R_f \cong R[x]/(fx-1)$
positive_passages.docid: 18036
positive_passages.text: Localization by a non-nilpotent as a polynomial quotient
negative_passages.docid: 23071
negative_passages.text: Showing that $f_0 (x_1, \ldots, x_m) \mathrm tr A =\displaystyle{ \sum_{i=1}^n} f_0(x_1, \ldots, Ax_i,\ldots, x_m)$
negative_passages.docid: 75653
negative_passages.text: Prove that $|f ''|\ge 4$
negative_passages.docid: 49806
negative_passages.text: Prove that $\frac{R/ \ker \phi}{(\ker \phi + J)/ \ker \phi} \cong \frac{S}{\phi(J)}$
negative_passages.docid: 62566
negative_passages.text: Does $X\times S^1\cong Y\times S^1$ imply that $X\times\mathbb R\cong Y\times\mathbb R$?
negative_passages.docid: 98587
negative_passages.text: $\mathbb Z [X] / (X)$ isomorphic to $\mathbb Z[X] / (X+1)$ isomorphic to $\mathbb Z [X] / (X+2015)$
negative_passages.docid: 41069
negative_passages.text: Justifying $\,\Bbb{Z}[i]/\langle 2\rangle\cong \Bbb{Z}[X]/\langle X^2+1,2\rangle\cong \Bbb{F}_2[X]/\langle X^2+1\rangle$
negative_passages.docid: 139595
negative_passages.text: Show that $(l_1)^* \cong l_{\infty}$
negative_passages.docid: 146334
negative_passages.text: Are there fields $F$ such that the rings $F[x]/(x^2)$ and $F[x]/(x^2-1)$ are isomorphic?
negative_passages.docid: 3296
negative_passages.text: Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
negative_passages.docid: 49166
negative_passages.text: $R^n \cong R^m$ iff $n=m$
negative_passages.docid: 14830
negative_passages.text: A transformation of F[x]
negative_passages.docid: 153869
negative_passages.text: Under what $p$, $-1$ is a square in $\mathbf F_p$?
negative_passages.docid: 93328
negative_passages.text: $\mathbb{F}_p[X]/(X^2+X+1)$ is a field iff $p \equiv 2 \bmod 3$
negative_passages.docid: 98816
negative_passages.text: How to prove that $\{f+g<a\}=\bigcup_{r\in{\Bbb Q}}(\{f<r\}\cap\{g<a-r\})$?
negative_passages.docid: 142699
negative_passages.text: Is $R/N(R)$ a faithfully flat $R$-module?
negative_passages.docid: 112089
negative_passages.text: Find the Maclaurin series of f(x)