Is $\mathbb{Z}[x]$ an integral domain? If so, why?
14158
Prove that $R$ is an integral domain $\Leftrightarrow$ $R[x]$ is an integral domain
77903
Finding the integral closure of $\mathbb{Z}$ in $\mathbb{Q}[i]$
102074
where does the term "integral domain" come from?
141410
Injective integral domains are fields
46047
Check whether the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$ is a field or an integral domain
119699
Examples of Cohen-Macaulay integral domains
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?
155745
Ideals of $\mathbb{Z}[X]$
150677
What are the integers $n$ such that $\mathbb{Z}[\sqrt{n}]$ is integrally closed?
132289
Associates in Integral Domain
153204
Euclidean domain $\mathbb{Z}[\sqrt{d}]$
154845
Irreducible elements in  $\mathbb{Z}[\sqrt{-2}]$ and is it a Euclidean domain?
78118
Algebraically, why is $\mathbb{Z}[i]/(i + 1)$ isomorphic to $\mathbb{Z}_{2}$?
32839
Example of integral domain with infinitely ascending chain of ideals.
58424
If $A$ an integral domain contains a field $K$ and $A$ over $K$ is a finite-dimensional vector space, then $A$ is a field.
93681
Integral closure of $\mathbb{Z}$ in $\mathbb{C}$ is not finitely generated as a $\mathbb{Z}$-module?
124672
Let $f:R\rightarrow S$ be a ring homomorphism. Prove or disprove: if $f$ is onto and $R$ is an integral domain, then $S$ is an integral domain