Why $ \mathbb{Z}[x]$ is not Principal Ideal Domain
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
138114
Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
19230
Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
92703
Proving that $\mathbb{Z}[x]$ and $\mathbb{Q}[x]$ are not isomorphic.
65536
Finitely generated ideals in a Boolean ring are principal, why?
132193
Why $\Bbb Z$ = (integers) is an integral domain?
24413
Why is $\mathbb{Z}[\sqrt{-n}], n\ge 3$ not a UFD?
120181
The ideal generated by $2$ and $ x$ in $\mathbb{Z}[x]$
78380
Dedekind domain with a finite number of prime ideals is principal
109691
When are kernels of homomorphisms on $\mathbb{Z}[x]$ principal ideals, and what does this have to do with Gauss's lemma?
33245
Show that every ideal of the ring $\mathbb Z$ is principal
108896
Prime ideal in a polynomial ring over an integrally closed domain
85032
$Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective
35569
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
90533
Show that if $p(x)$ is reducible in $F[x]$, then $F[x]/(p(x))$ is not an integral domain.
57669
A proof that $\mathbb{Z}_{p}$ is an integral domain if and only if $p$ is prime.
42170
$R$ integral domain where every prime ideal is principal then set of non-principal ideals has maximal element