Is it true that two polynomial rings are not isomorphic iff the rings are not isomorphic?
18330
Does $R[x] \cong S[x]$ imply $R \cong S$?
116594
Finite fields are isomorphic
28327
(Simple) Examples on Non-Commutative Rings
78118
Algebraically, why is $\mathbb{Z}[i]/(i + 1)$ isomorphic to $\mathbb{Z}_{2}$?
151287
Isomorphic abelian groups which are not isomorphic R-modules
30714
A question on ring homomorphisms and maximal ideals.
42810
Is $(\mathbb{Q},+)$ isomorphic to $(\mathbb{Q}^n,+)$?
75558
Counter-example for prime ideals in a non commutative ring.
142352
how to prove $G_1$ and $G_2$ aren't isomorphic?
153291
Why a ring homomorphism from a local ring will not map a non-unit to a unit？
86015
$\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
12110
How are $2\mathbb{Z}\ncong3\mathbb{Z}$ different as rings?
61491
Complex Ring Isomorphism
87160
Prove $\mathbb{Z}_3[x]/(x^2+1)$ and $\mathbb{Z}_3[x]/(x^2+x-1)$ are isomorphic.
7010
Example of two non-isomorphic fields which embed inside each other
146356
To prove two sets are isomorphic is it sufficient to find 2 injections or 2 surjections?
121465
$R[x]$ has a subring isomorphic to $R$.