Can a commutative ring $R$ with identity be isomorphic to the product ring $R\times R$?
22604
Can $R \times R$ be isomorphic to $R$ as rings?
128493
Given a commutative ring $R$ and an epimorphism of free modules $R^m \to R^n$ is then $m \geq n$?
41846
$(\mathbb{R}^n,\|\cdot\|_{p})$ is isometrically isomorphic to $(\mathbb{R}^n,\|\cdot\|_{q})$ iff $p=q,$
45179
When does the isomorphism $G\simeq \ker(\phi)\times \operatorname{im}(\phi)$? hold?
128989
Is ${\bf Z} \times {\bf Z}$ elementarily equivalent to ${\bf Z}$?
121465
$R[x]$ has a subring isomorphic to $R$.
62711
Canonical map $R/(I\cap J)\rightarrow R/I\times _{R/(I+J)} R/J$ is an isomorphism
155445
What kind of ring $R$ makes $\mathcal O(\mathrm{Proj}\,R[x_0,\cdots,x_n])=R$?
33283
Every Artinian ring is isomorphic to a direct product of Artinian local rings
114394
Determine whether $\mathbb{Z}\times \mathbb{Z}$ and $\mathbb{Z}\times \mathbb{Z}\times \mathbb{Z}$ are isomorphic groups or not.
137011
showing $\psi: R\to \mathbb C$ is ring isomorphism.
75520
If $a^3 =a$ for all $a$ in a ring $R$, then $R$ is commutative.
120035
Pattern in Isomorphisms between $\mathbb Z_m \times \mathbb Z_n$ and $\mathbb Z_{mn}$
146334
Are there fields $F$ such that the rings $F[x]/(x^2)$ and $F[x]/(x^2-1)$ are isomorphic?
44983
Isomorphism of R-modules
156878
If every commutator is idempotent, then the ring is commutative
135699
Questions about a commutative ring with exactly three ideals