Let $d$ be a square free integer. Show that $\mathbb{Z}[\sqrt{d}]$ is an integral domain.
62951
Is there a more direct way of proving that this ring is an integral domain?
17859
Showing $F[x,y]/(ax^2+by^2-1)$ is a Dedekind domain
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?
86807
The units of $\mathbb Z[\sqrt{2}]$
95863
Describe the units in $\mathbb{Z}[\sqrt{-d}]$
52081
Why is not the ring $\mathbb{Z}[2\sqrt{2}]$ a unique factorization domain?
58717
Why isn't $\mathbb Z [\sqrt{pq}]$ a factorial domain
19230
Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
108896
Prime ideal in a polynomial ring over an integrally closed domain
60665
Meaning of $\mathbb{Z}\left[\sqrt{3}\right]$?
42170
$R$ integral domain where every prime ideal is principal then set of non-principal ideals has maximal element
139463
Commutative integral domain does not finitely generate its field of fractions
25397
Prove $R \times R$ is NOT an integral domain
8317
Understanding a proof of "If $R$ is an integral domain, then $R[x]$ is an integral domain as well".
76501
How can we show that $\mathbb Q$ is not a free $\mathbb Z$-module?
93029
Prove that when $d$ is in $\mathbb{Q} \setminus\mathbb{Z}$, $\mathbb{Z}[\sqrt{d}]$ is not a finitely generated abelian group.
67699
Integral domain that is integrally closed, one-dimensional and not noetherian