Prove or disprove: $ \mathbb{Q} \times \mathbb{Q[i]}$ is integral domain
37960
Zero Divisors in Direct Product of Rings
134458
Isomorphisms preserving integral domains and fields
135152
Non-UFD integral domain such that prime is equivalent to irreducible?
94579
$\mathbb{Q}[x,y]/\langle x^2+y^2-1 \rangle$ is an integral domain, and its field of fractions is isomorphic to $\mathbb Q(t)$
139463
Commutative integral domain does not finitely generate its field of fractions
128989
Is ${\bf Z} \times {\bf Z}$ elementarily equivalent to ${\bf Z}$?
141659
Every field is an integral domain
4196
A valid proof for the invariance of domain theorem?
151786
Proving that there is no ideal $I$ in $\mathbb{Z}[t]$ such that $\mathbb{Z}[t]/I \cong \mathbb{Q}$
154845
Irreducible elements in  $\mathbb{Z}[\sqrt{-2}]$ and is it a Euclidean domain?
57669
A proof that $\mathbb{Z}_{p}$ is an integral domain if and only if $p$ is prime.
149783
$\mathbb Z\times\mathbb Z$ is principal but is not a PID
1020
Proving that $\mathbb{Z}[\sqrt{2}]$ is a Euclidean domain
41035
Mapping that proves $\mathbb{Z} \subset \mathbb{Q}$
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
23721
Prove that the Gaussian Integer's ring is a Euclidean domain
81982
Is $\mathbb{Z}[x]$ a principal ideal domain?