Is $\mathbb{Z}[2\sqrt{2}]$ a PID?
52081
Why is not the ring $\mathbb{Z}[2\sqrt{2}]$ a unique factorization domain?
102282
Let $R$ be a PID, and let $\pi\in R$ be prime. Is it $R/\langle\pi\rangle \times R/\langle \pi\rangle$ a cyclic $R$-module?
76202
Sufficient conditions for being a PID
133775
Is $\mathbb{Z}[\sqrt{-7}]$ a UFD or not?
87617
Ring of $\mathbb{Z}_2$-valued functions
120699
Is $\mathcal{O}_{\mathbb{Q}(\sqrt{5})} = \mathbb{Z}[\phi]$?
11935
Is $\mathbb{Z} \left[ \frac{1+i \sqrt{7}}{2} \right]$ euclidean?
24413
Why is $\mathbb{Z}[\sqrt{-n}], n\ge 3$ not a UFD?
51687
Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
34754
Why is the polynomial ring of more than one variable not a PID?
84017
Is $\sqrt[3]{2}$ contained in $\mathbb{Q}(\zeta_n)$?
121845
Quotient of polynomials, PID but not Euclidean domain?
24931
Is the localization of a PID a PID?
7500
$\arctan$ of a square root as a rational multiple of $\pi$
153204
Euclidean domain $\mathbb{Z}[\sqrt{d}]$
86515
Characterization of integers which has a $2$-adic square root
138944
Is $\mathbb Z[\sqrt{-3}]$ Euclidean under some other norm?