$[a,b)$ and $(a,b)$ are not homeomorphic
36921
An Open Interval and a Half-open Interval are not Homeomorphic
107091
Taking the automorphism group of a group is not functorial.
92599
Prove there generally is no isomorphism between $R[x]/(x^2-a)$ and $R^2$
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
117185
The union of a strictly increasing sequence of $\sigma$-algebras is not a $\sigma$-algebra
26749
$\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$
94747
Show that the rings $2\mathbb{Z}$ and $3\mathbb{Z}$ are not isomorphic.
70712
How to prove that $k[x, xy, xy^2, \dotsc]$ is not noetherian?
122012
The ideal $(x,y)$ is not a free $K[x,y]$-module
114640
Showing that an ideal is not a free $R-$module.
85032
$Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective
155604
Show that $k[x,y]/(xy-1)$ is not isomorphic to a polynomial ring in one variable.
83595
Proving that $\mathbb{A}=\{\alpha \in \mathbb{C}: \alpha \text{ is algebraic over } \mathbb{Q} \}$ is not a finite extension
144072
Are the spaces $\mathbb{H}^n$ and $\overline{\mathbb{R}}^n_+$ homeomorphic?
99884
Are $\mathbb{Q}_p$ and $\mathbb{Q}_q$ homeomorphic?
86537
Prove that an open interval and a closed interval are not homeomorphic
148616
When is a ring homomorphism $A \to A$ surjective but not injective.