Show that $(\mathbb{Z}\oplus\mathbb{Z})[x]$ is not isomorphic to $\mathbb{Z}[x]\oplus\mathbb{Z}[x] $ .
128711
$(\Bbb Z\oplus \Bbb Z)[X] \not\cong \Bbb Z[X]\oplus \Bbb Z[X]\,$?
83001
Easier way to show $(\mathbb{Z}/(n))[x]$ and $\mathbb{Z}[x] / (n)$ are isomorphic
18484
Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
93169
Show that $(\mathbb Z[x],+)$ and $(\mathbb Q_{>0},\cdot)$ are isomorphic groups
26749
$\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$
135611
Extensions of $\mathbb{Z}$ by $\mathbb{Z}$
104486
Ideal in $\mathbb Z[x]$ which is not two-generated
129732
What is $\operatorname{Aut}(\mathbb{Z}_2\oplus \mathbb{Z}_2)$?
33781
Is $\mathbb{Z}[x]/(x^2+1)$ isomorphic to $\mathbb{Z}[i]$?
155604
Show that $k[x,y]/(xy-1)$ is not isomorphic to a polynomial ring in one variable.
17991
Nonconstant polynomials do not generate maximal ideals in $\mathbb Z[x]$
81238
Is $O(2)$ really not isomorphic to $SO(2)\times \{-1,1\}$?
94747
Show that the rings $2\mathbb{Z}$ and $3\mathbb{Z}$ are not isomorphic.
45432
Showing that $f:(0,2\pi]\to S^1$ is not a homeomorphism
57310
Prove $\mathbb{Z}$ is not a vector space over a field
71173
Show that $\mathbb{A}^n$ on the Zariski Topology is not Hausdorff, but it is $T_1$
99032
Prove that the additive group of $\mathbb{Z}[x]$ is isomorphic to the group of positive rational numbers under multiplication.