$\mathbb{C}[x,y,z]/(xy-z^2)$ is not a field
46047
Check whether the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$ is a field or an integral domain
132386
Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic
144572
Proof that ideals in $C[0,1]$ are of the form $M_c$ that should not involve Zorn's Lemma
58009
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
18484
Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
55026
$\mathbb{Q}[X,Y]/(Y^2-X^3)$ is not a UFD
158502
Showing $\sin(\bar{z})$ is not analytic at any point of $\mathbb{C}$
35777
$\mathbb{R}[X,Y]/(Y-X^2,Y+X)\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$
122012
The ideal $(x,y)$ is not a free $K[x,y]$-module
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
116630
Antiderivative $1/z$ on $\mathbb C$
108955
Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
88474
$\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
13262
$\mathbb{R}P^4$ and $\mathbb{R}P^6$ do not admit fields of tangent $2$-planes
98577
Show that the set $\mathbb{Q}(\sqrt{p})=\{a+b\sqrt{p}; a,b,p\in\mathbb{Q},\sqrt{p}\notin \mathbb{Q}\}$ is a field
109610
Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
86234
Explain why $\mathbb{Z \times Z}$ and $\mathbb{R \times R}$ is not a field