$\mathbb{Z}_p$ with $p$ prime is integral domain
57669
A proof that $\mathbb{Z}_{p}$ is an integral domain if and only if $p$ is prime.
109199
Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$
112345
In an Integral Domain is it true that $\gcd(ac,ab) = a\gcd(c,b)$?
101637
Let $R$ be an integral domain. If $x \in R$ is prime, then $x$ is irreducible.
151985
If $p$ is a prime and $x,y \in \mathbb{Z}$, then $(x+y)^p \equiv x^p+y^p \pmod{p}$
78950
Does this map extend to a unique automorphism of the polynomial ring of an integral domain?
136855
Proof that $\mathbb{Z}\left[\frac{1 + \sqrt{-19}}{2}\right]$ is a PID
62951
Is there a more direct way of proving that this ring is an integral domain?
74139
Subrings of integral domains have the same identity element.
87780
Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither?
137858
Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?
133636
Is $\mathbb Z[X]/(X^2-1)$ a domain?
44083
prove that maximal ideal in $\mathbb{Z}$ generated by a prime number
76496
Showing that every field is an integral domain.
108896
Prime ideal in a polynomial ring over an integrally closed domain
150677
What are the integers $n$ such that $\mathbb{Z}[\sqrt{n}]$ is integrally closed?
94819
Prove that $\frac{\mathbb{C}[x,y]}{\langle x^2-y^2-1\rangle}$ is an integral domain such that all the nonzero prime ideals are maximal.