The localisation of the ring $\mathbb{Z}$ at the prime ideal $(p)$ is PID
57138
Localization of a UFD that is a PID
84386
Domain strictly contained in the intersection of localizations at the primes of height one
109691
When are kernels of homomorphisms on $\mathbb{Z}[x]$ principal ideals, and what does this have to do with Gauss's lemma?
155745
Ideals of $\mathbb{Z}[X]$
154239
Can a prime in a Dedekind domain be contained in the union of the other prime ideals?
83050
Show that $P[x]+\langle x\rangle $ is a prime ideal of $R[x]$.
19230
Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
63447
Prove that the kernel of a homomorphism is a principal ideal. (Artin, Exercise 9.13)
111996
Maximal and Prime Ideal in Z
145879
$R$ is PID, so $R/I$ is PID, and application on $\mathbb{Z}$ and $\mathbb{N}$
21946
What do prime ideals in $k[x,y]$ look like?
90889
Prime ideals in a finite direct product of rings
22544
Let R be a commutative ring, and let P be a prime ideal of R. Suppose that P has no nontrivial zero divisors in it. Show that R is an integral domain.
97740
Homogeneous ideals are contained in homogeneous prime ideals
74558
Localization of ideals at all primes
21604
A complete ring with respect to an ideal
50412
Prime elements in $\mathbb{Z}/n\mathbb{Z}$