Examples where $R/I\cong R$?
93670
A surjective endomorphism (of a Noetherian ring) is injective.
40094
Does $G\oplus G \cong H\oplus H$ imply $G\cong H$ in general?
147564
Why does $(A/I)\otimes_R (B/J)\cong(A\otimes_R B)/(I\otimes_R 1+1\otimes_R J)$?
122958
$R/I$ is commutative iff $rs-sr \in I$
25764
Example of a ring such that $R^2\simeq R^3$, but $R\not\simeq R^2$ (as $R$-modules)
63701
An example of a regular function over an open set
77297
Counterexample for $A,B\triangleleft G,G/A\cong B \Rightarrow G/B\cong A$
35188
Counterexample: $G \times K \cong H \times K \implies G \cong H$
133495
Example of a ring without Invariant Basis Property
113898
Why is that $\widehat{\mathbb{R}/\mathbb{Z}}\cong\mathbb{Z}$?
14322
Examples of bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$
42835
Example of a relation that is symmetric and transitive, but not reflexive
34798
Example of element of double dual that is not an evaluation map
148569
Embeddings $A → B → A$, but $A \not\cong B$?
98352
If $k|n$, then $D_{2n}/\langle{r^k}\rangle\cong D_{2k}$
42774
Examples of involutions on $\mathbb{R}$
58766
free groups: $F_X\cong F_Y\Rightarrow|X|=|Y|$