$\Bbb{C} \otimes_{\Bbb{R}} \Bbb{C}$ and $\Bbb{C} \otimes_{\Bbb{C}} \Bbb{C}$ are not isomorphic as $\Bbb{R}$-vector spaces
6101
Are $\mathbb{C} \otimes _\mathbb{R} \mathbb{C}$ and $\mathbb{C} \otimes _\mathbb{C} \mathbb{C}$ isomorphic as $\mathbb{R}$-vector spaces?
5996
Are $(\mathbb{R},+)$ and $(\mathbb{C},+)$ isomorphic as additive groups?
120035
Pattern in Isomorphisms between $\mathbb Z_m \times \mathbb Z_n$ and $\mathbb Z_{mn}$
102284
$GL(n,\mathbb R)/SL(n,\mathbb R)$ is isomophic to $\mathbb R^\times$
142352
how to prove $G_1$ and $G_2$ aren't isomorphic?
18343
Counting homomorphisms between $\Bbb Z$ and $\Bbb Z_n$ and also between $\Bbb Z_n$ and $\Bbb Q$
132386
Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic
88474
$\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
109610
Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
94747
Show that the rings $2\mathbb{Z}$ and $3\mathbb{Z}$ are not isomorphic.
137029
Prove that $\operatorname{Hom}_{\Bbb{Z}}(\Bbb{Q},\Bbb{Z}) = 0$ and show that $\Bbb{Q}$ is not a projective $\Bbb{Z}$-module.
40321
$\operatorname{Aut}(\mathbb Z_n)$ is isomorphic to $U_n$.
26497
Take $\mathbb{R}$ as a vector space over $\mathbb{Q}$, then a basis for $\mathbb{R}$, then $|B|=2^{\aleph_0}$
91222
Isomorphism between $\mathfrak o(4,\mathbb R)$ and $\mathfrak o (3,\mathbb R) \oplus\mathfrak o (3,\mathbb R) $
108955
Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
62635
Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.
92211
When are $\mathbb Z_m$ and $\mathbb Z_n$ homomorphic?