$A_f\cong A[T]/(Tf-1)$
42552
Localisation is isomorphic to a quotient of polynomial ring
158327
#define f(g,g2) g##g2
118299
Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$
147564
Why does $(A/I)\otimes_R (B/J)\cong(A\otimes_R B)/(I\otimes_R 1+1\otimes_R J)$?
138069
Proof that $\bigcap_{a\in A} \bigg(\, \bigcup_{b\in B} F_{a,b} \, \bigg) = \bigcup_{f\in ^AB} \bigg(\, \bigcap_{a \in A} F_{a,f(a)}\,\bigg) $
153406
$[F(t):F(t^n)]=n$ where $t$ is trascendental
102485
Showing that a topological space is ${\rm T}_1$
17191
How to verify $H\otimes K \cong \bigoplus\limits_{i\in I}H$
25050
To prove that $(F,+)$ and $(F-\{0\},\cdot)$ are not isomorphic as groups.
88928
$F:G\to B$ is an isomorphism between groups implies $F^{-1}$ is an isomorphism
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
53432
What is the algebraic closure of $\mathbb F_q$?
141258
Why does $M \mathbin{\otimes_R} N \cong M_\mathfrak{p} \mathbin{\otimes_{R_\mathfrak{p}}} N$?
147627
Relation between condition numbers $\kappa(A^T A)$ and $\kappa(A)$
95806
Proving commutativity of convolution $(f \ast g)(x) = (g \ast f)(x)$
119793
Proving that $D_{12}\cong S_3 \times C_2$
34670
What exactly is the fixed field of the map $t\mapsto t+1$ in $k(t)$?