Show that $\mathbb Q[x]/(x^2+2)$ and $\mathbb Q[x]/(x^2-2)$ are not isomorphic.
38549
$\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$
96363
How to show that $\mathbb R^n$ with the $1$-norm is not isometric to $\mathbb R^n$ with the infinity norm for $n>2$?
119545
Nonzero rationals under multiplication are not a cyclic group
133312
Are these polynomials irreducible in $\mathbb{Q}[x]$?
30753
Showing there is no ring whose additive group is isomorphic to $\mathbb{Q}/\mathbb{Z}$
33370
Show that the one point compactification of $\mathbb{Q}$ is not Hausdorff
2348
Show that the sphere, S, and $\mathbb{R}^2$ is not homeomorphic
83001
Easier way to show $(\mathbb{Z}/(n))[x]$ and $\mathbb{Z}[x] / (n)$ are isomorphic
98731
Show that there is no epimorphism from ($\mathbb{Q}$, +) to ($\mathbb{Z}$, +)
55050
How to show that $\mathbb{Q}(i,\sqrt[4]{1+i} )$ is not contained in any cyclotomic extension of $\mathbb{Q}(i)$?
41872
Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$
36142
What is $\mathbb Z \oplus \mathbb Z / \langle (2,2) \rangle$ isomorphic to?
83595
Proving that $\mathbb{A}=\{\alpha \in \mathbb{C}: \alpha \text{ is algebraic over } \mathbb{Q} \}$ is not a finite extension
79056
Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
39114
Prove that a set in $\mathbb R^3$ is not an algebraic set
4228
Prove that the only automorphism of $\mathbb{Q}(\sqrt[3]{2})$ is the identity automorphism.
95764
Prove that the additive groups $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic.