Find an element $p$ which is an irreducible element but the ideal $\langle p\rangle $ is not a maximal ideal?
68202
Must an ideal generated by an irreducible element be a maximal ideal?
42170
$R$ integral domain where every prime ideal is principal then set of non-principal ideals has maximal element
20790
What are irreducibles in the ring $R$ of entire functions?
91627
What is a primary decomposition of the ideal $I = \langle xy, x - yz \rangle$?
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
18336
$x^p-c$ has no root in a field $F$ if and only if $x^p-c$ is irreducible?
97902
In a integral domain every prime element is irreducible
111935
Irreducible but not prime
135102
How do the definitions of "irreducible" and "prime" elements differ?
101637
Let $R$ be an integral domain. If $x \in R$ is prime, then $x$ is irreducible.
96071
How to show that a prime ideal of height 2 can’t necessarily be generated by 2 elements? (Hartshorne exercise I.1.11)
20296
The ideal $I= \langle x,y \rangle\subset k[x,y]$ is not principal
133975
Localising a polynomial ring and non-maximal prime ideal
54916
Maximal ideal in commutative ring
115920
Showing $R$ is a local ring if and only if all elements of $R$ that are not units form an ideal
141687
Nonprincipal prime ideals contain two relatively prime elements
104486
Ideal in $\mathbb Z[x]$ which is not two-generated