Is a localization of a UFD at a prime ideal a PID?
57138
Localization of a UFD that is a PID
138882
A prime poset of ideals
16984
Finite extension of domains : preimage of non-zero ideal is non-zero?
78380
Dedekind domain with a finite number of prime ideals is principal
76661
Checking the maximality of a principal ideal in $R[x]$
136855
Proof that $\mathbb{Z}\left[\frac{1 + \sqrt{-19}}{2}\right]$ is a PID
18036
Localization by a non-nilpotent as a polynomial quotient
34754
Why is the polynomial ring of more than one variable not a PID?
67669
Prime ideals of a finite direct product ring
3037
Integral domain without unity has prime characteristic?
74558
Localization of ideals at all primes
62917
Associated Prime Ideals in a Noetherian Ring; Exercise 6.4 in Matsumura
29359
Localisation isomorphic to a quotient of polynomial ring
154239
Can a prime in a Dedekind domain be contained in the union of the other prime ideals?
98818
Quotient ring of a localization of a ring
108896
Prime ideal in a polynomial ring over an integrally closed domain
18484
Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.