Show that $\mathbb{Q}[x]/\langle x^2-x\rangle$ is not a domain
90533
Show that if $p(x)$ is reducible in $F[x]$, then $F[x]/(p(x))$ is not an integral domain.
68014
Prove that $\mathfrak{su}(2)$ is not isomorphic to $\mathfrak{sl}(2,\mathbb R)$
76501
How can we show that $\mathbb Q$ is not a free $\mathbb Z$-module?
91622
Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.
153444
$\mathbb{Q}(\sqrt[3]{2})$ is not in any cyclotomic extension of $\mathbb{Q}$
2907
How do I show that $x$ is a root of $p(x)$ in $F[x]/\langle p(x)\rangle$?
139463
Commutative integral domain does not finitely generate its field of fractions
106911
Square root of $-1$ in the ring $\mathbb{R}[x]/\langle(x^2+1)^2\rangle$
11710
How to show that $\mathbb{Q}$ is not $G_\delta$
25397
Prove $R \times R$ is NOT an integral domain
104300
Help justifying that $\mathbb Q(\sqrt[3]{2})$ is not a splitting field over $\mathbb Q$.
137285
Prove $\mathbb{Z}_2 \times \mathbb{Z}_2$ is not isomorphic to $\mathbb{Z}_4$
139288
Formal proof that $e^x$ is not algebraic
2348
Show that the sphere, S, and $\mathbb{R}^2$ is not homeomorphic
108955
Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
75639
Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$
17859
Showing $F[x,y]/(ax^2+by^2-1)$ is a Dedekind domain