How to show that $\Bbb Z[x,y,z,w]/(xw-zy)$ is not a UFD
85987
Prove that $k[x,y,z,w]/(xy-zw)$, the coordinate ring of $V(xy-zw) \subset \mathbb{A}^4$, is not a unique factorization domain
77735
When $\Bbb Z_n$ is a domain. Counterexample to $ab \equiv 0 \Rightarrow a\equiv 0$ or $b\equiv 0\pmod n$
85398
$\mathsf{ZF}$ is not finitely axiomatizable
155604
Show that $k[x,y]/(xy-1)$ is not isomorphic to a polynomial ring in one variable.
83713
If $z,w\in \mathbb{C}^{\times}$, then $|z+w|=|z|+|w|$ iff $w=tz$ for some $t\gt 0$
30511
Monic $f(x)\in\Bbb Z[x]$ has no rational root if $f(0)\ \&\ f(1)$ odd [Parity Root Test, Modular Root Test]
156727
A step in the proof of Characterization of $W^{1,\infty}$
75970
$\mathbb Z[1/2]$ is not finitely generated?
46917
How to prove that $GL(n,\mathbb R)$ is not connected subset and open subset of$M_n (\mathbb{R})$
35569
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
31451
Proving a subring of $\mathbb{Q}$ containing $\mathbb{Z}$ is a PID
39583
ii) Show that $u$ is not a real part of the function which analytic on $\mathbb{C} \backslash \lbrace 0 \rbrace$
66238
Proving $\mathbb{Z}[\sqrt {10}]$ is not a UFD
101453
Existence of a Boolean algebra with a unique ultrafilter in ZF
23517
Presentation $\langle x,y,z\mid xyx^{-1}y^{-2},yzy^{-1}z^{-2},zxz^{-1}x^{-2}\rangle$ of group equal to trivial group
28452
Statement that is provable in $ZFC+CH$ yet unprovable in $ZFC+\lnot CH$
61226
Group Structure on $\Bbb R$