$\mathbb{Z}[\sqrt{-7}]$ is UFD?
133775
Is $\mathbb{Z}[\sqrt{-7}]$ a UFD or not?
140497
Irreducibles are prime in a UFD
8087
Algebraic integers of $\mathbb{Q}(\sqrt{m})$ for $m$ a squarefree integer
86807
The units of $\mathbb Z[\sqrt{2}]$
236
Proof of general Euclid's Lemma in a UFD (by Euclidean algorithm?)
153664
When is $\Bbb{Z[\zeta_n]}$ a PID?
152109
In a UFD if $x$ is irreducible, then $(x)$ is prime
93291
Method for determining irreducibles and factorising in $\mathbb Z[\sqrt{d}]$
145879
$R$ is PID, so $R/I$ is PID, and application on $\mathbb{Z}$ and $\mathbb{N}$
55026
$\mathbb{Q}[X,Y]/(Y^2-X^3)$ is not a UFD
24351
The ring $\Bbb Z\left [\frac{-1+\sqrt{-19}}{2}\right ]$ is not a Euclidean domain
133636
Is $\mathbb Z[X]/(X^2-1)$ a domain?
129521
Is $\sqrt[3]{5}$ in $\mathbb Q(\sqrt[3]{2})$?
114152
Intermediate fields between $\mathbb{Z}_2 (\sqrt{x},\sqrt{y})$ and $\mathbb{Z}_2 (x,y)$
57101
About the localization of a UFD
4105
Irreducible but not prime in $\mathbb{Z}[\sqrt{-5}] $
154845
Irreducible elements in  $\mathbb{Z}[\sqrt{-2}]$ and is it a Euclidean domain?