$k[x,y]/(xy-1)$ isomorphic to $k[x,\frac{1}{x}]$
42552
Localisation is isomorphic to a quotient of polynomial ring
17859
Showing $F[x,y]/(ax^2+by^2-1)$ is a Dedekind domain
107163
Proof that $S_3$ isomorphic to $D_3$
35777
$\mathbb{R}[X,Y]/(Y-X^2,Y+X)\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$
48291
Proof that $\mathrm{ker}(f^*) = \mathrm{im}(f)^{\perp} $
93169
Show that $(\mathbb Z[x],+)$ and $(\mathbb Q_{>0},\cdot)$ are isomorphic groups
49806
Prove that $\frac{R/ \ker \phi}{(\ker \phi + J)/ \ker \phi} \cong \frac{S}{\phi(J)}$
102371
Proving that two vector spaces of equal dimension are isomorphic
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
40400
Finding an isomorphism between $\mathbb{Z}[i]/(7)$ and $\mathbb{Z}[\sqrt{-2}]/(7)$
50130
$\operatorname{Aut}(V)$ is isomorphic to $S_3$
93118
How to show that if two integral domains are isomorphic, then their corresponding field of quotients are isomorphic?
135046
Can this quick way of showing that $K[X,Y]/(Y-X^2)\cong K[X]$ be turned into a valid argument?
21946
What do prime ideals in $k[x,y]$ look like?
106091
Showing $\mathcal{P}(X)$ is isomorphic to $2^X$
25383
Morphism between quotient sheaf ($K_{X}/\mathcal{O}_{X}$) and $\bigoplus_{x\in\mathcal{X}}i_{x,*}(K(X)/\mathcal{O}_{X,x})$
109596
Isomorphism from $\mathrm{Aut}(\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z})$ to $S_3$