Is $k[x,y,z]/(y^2-xz)$ a UFD?
18484
Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
57101
About the localization of a UFD
87101
Irreducible but not prime in $K[X,Y]/(X^2-Y^3)$
15626
Relations of a~b iff b = ak^2
133775
Is $\mathbb{Z}[\sqrt{-7}]$ a UFD or not?
133636
Is $\mathbb Z[X]/(X^2-1)$ a domain?
63410
Proof on showing if F(x,y,z)=0 then product of partial derivatives (evaluated at an assigned coordinate) is -1
83798
Does $A$ a UFD imply that  $A[T]$ is also a UFD?
77464
Prove that ${x dy - y d x\over x^2 + y^2}$ is not exact
51769
If $x,y,z\in[-1,1]$ and $1+2xyz\geq x^2+y^2+z^2$, then can we infer $1+2(xyz)^n\geq x^{2n}+y^{2n}+z^{2n}$?
135046
Can this quick way of showing that $K[X,Y]/(Y-X^2)\cong K[X]$ be turned into a valid argument?
1712
$ d_1,d_2\mid n\iff {\rm lcm}(d_1,d_2)\mid n\ $ [LCM Universal Property]
127000
When does $V = \ker(f) \oplus \operatorname{im}(f)$?
152109
In a UFD if $x$ is irreducible, then $(x)$ is prime
147627
Relation between condition numbers $\kappa(A^T A)$ and $\kappa(A)$
75466
During U-substitution, is the $du$ that we use as the infinitesimal in $\int f(u) \ du$ changing size?
158353
If $F=K(u,v)$ with $u^p$,$v^p\in K$ and $[F:K]=p^2$, $\operatorname{char} K=p>0$, then $F$ is not a simple extension of $K$.