Is $\mathbb{Z}[\sqrt 2 , \sqrt 3]$ an integral domain?
93621
Prove that $\mathbb{Z}[\omega]$ is an integral domain
19230
Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
44307
Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
141410
Injective integral domains are fields
133775
Is $\mathbb{Z}[\sqrt{-7}]$ a UFD or not?
154845
Irreducible elements in  $\mathbb{Z}[\sqrt{-2}]$ and is it a Euclidean domain?
99835
Polynomial in $\mathbb{Q}[x]$ with root $\sqrt[3]{2}+\sqrt[3]{3}$
76496
Showing that every field is an integral domain.
53331
$\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$
104300
Help justifying that $\mathbb Q(\sqrt[3]{2})$ is not a splitting field over $\mathbb Q$.
86807
The units of $\mathbb Z[\sqrt{2}]$
120181
The ideal generated by $2$ and $ x$ in $\mathbb{Z}[x]$
3037
Integral domain without unity has prime characteristic?
33781
Is $\mathbb{Z}[x]/(x^2+1)$ isomorphic to $\mathbb{Z}[i]$?
147722
Is there a nice example of integral domain $R$ and $s,t \in R$, with $Rs \cap Rt$ not principal but lcm($s,t$) exists?
142336
Why does the integral domain "being trapped between a finite field extension" implies that it is a field?
141659
Every field is an integral domain