If $R[x]$ and $R[[x]]$ are isomorphic, then are they isomorphic to $R$ as well?
90071
Why don't we have an isomorphism between $R[x]$ and $ R[[x]]$?
55902
Show $R[x]/(x)\cong R$
145722
Prove there is a bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.
146356
To prove two sets are isomorphic is it sufficient to find 2 injections or 2 surjections?
158311
What is the dimension of $R[[X]]$ where $R$ is a Noetherian ring?
120811
What does "isomorphic" mean in linear algebra?
122958
$R/I$ is commutative iff $rs-sr \in I$
17670
If $p\in R[X_1,\dots,X_n]$ is irreducible, is it still irreducible in $R[X_1,\dots,X_n,\dots,X_N]$?
140883
If $R$ is a local ring, is $R[[x]]$ (the ring of formal power series) also a local ring?
22604
Can $R \times R$ be isomorphic to $R$ as rings?
57166
Showing that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$ question
79734
Is every sub-lattice of $\mathcal P(X)$ isomorphic to a sub-lattice of $\mathcal P(X')$ containing singleton sets?
46841
When is a graph isomorphic to the source?
48537
If $\forall x \in R, x^2-x \in Z(G)$, than $R$ is commutative
144442
Let $R$ be a commutative unital ring. Is it true that the group of units of $R$ is not isomorphic with the additive group of $R$?
118073
Is the ring $m\mathbb{Z}$ isomorphic to the ring $n\mathbb{Z}$?
70872
Isomorphism of quotient modules implies isomorphism of submodules?