Prove that $R x R$ is not isomorphic to $R[x]/(x^2)$
92599
Prove there generally is no isomorphism between $R[x]/(x^2-a)$ and $R^2$
68014
Prove that $\mathfrak{su}(2)$ is not isomorphic to $\mathfrak{sl}(2,\mathbb R)$
114813
Proof: in $\mathbb{R}$, $((0,1),|\cdot|)$ is not compact.
90071
Why don't we have an isomorphism between $R[x]$ and $ R[[x]]$?
18330
Does $R[x] \cong S[x]$ imply $R \cong S$?
85092
Proving $ f(x) = x^2 $ is not uniformly continuous on the real line
88645
Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
26749
$\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$
82771
Proving that any polynomial $p:\mathbb{R}\rightarrow \mathbb{R}$ is not bounded, but its restriction to any bounded set is bounded
84707
How to prove a cross is not locally homeomorphic to an euclidean space?
86015
$\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
151803
Prove that $R$ is commutative
132386
Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic
64130
Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$
35953
Prove that a function is not injective
63453
A proof of the fact that the Fourier transform is not surjective from $\mathcal{L}^1(\mathbb{R})$ to $C_0( \mathbb{R})$
73248
Prove that $\mathbb{R^*}$, the set of all real numbers except $0$, is not a cyclic group