$I$ an irreducible ideal in a PID is a prime ideal
138851
Euclid's Lemma in a PID: irreducibles are prime: $ \pi\mid ab\Rightarrow \pi\mid a\,$ or $\pi\mid b$
87101
Irreducible but not prime in $K[X,Y]/(X^2-Y^3)$
78380
Dedekind domain with a finite number of prime ideals is principal
155991
Is it the case that every quotient ring ${F[x]}/{(p(x))}$ is a PID?
6507
Every prime ideal of height 1 in a UFD is principal
112045
A property of minimal prime ideal
21946
What do prime ideals in $k[x,y]$ look like?
67342
Why does a minimal prime ideal consist of zerodivisors?
154239
Can a prime in a Dedekind domain be contained in the union of the other prime ideals?
31049
If $p$ is an irreducible element of an integral domain $D$, and if $e$ belongs to $D^\ast$ prove that $ep$ is also ireducible
72230
Equivalence of definitions of prime ideal in commutative ring
49303
In a noetherian integral domain every non invertible element is a product of irreducible elements
68202
Must an ideal generated by an irreducible element be a maximal ideal?
67944
Nilpotent Elements and Intersection of Prime Ideals
31585
Primary ideals of $\mathbb{Z}$
145879
$R$ is PID, so $R/I$ is PID, and application on $\mathbb{Z}$ and $\mathbb{N}$
148434
Ring where irreducibles are primes which is not an UFD