Showing every prime ideal is maximal.
130466
Proving every prime ideal is maximal in a finite dimensional ring over a field.
110984
Ideals and prime ideals in a commutative ring.
52602
$K[X^2,X^3]\subset K[X]$ is a Noetherian domain and all its prime ideals are maximal
33245
Show that every ideal of the ring $\mathbb Z$ is principal
18406
An ideal whose radical is maximal is primary
149747
Prove that if I is a prime ideal of R then I[x] is a prime ideal of R[x]
108380
Assume $P$ is a prime ideal s.t. $K \subset P$, show $f(P)$ is a prime ideal
151829
Why are maximal ideals prime?
124151
Finite ring extension and number of maximal ideals
119056
If in a UFD every maximal ideal is principal then it is a PID
54916
Maximal ideal in commutative ring
6699
An ideal that is maximal among non-finitely generated ideals is prime.
42170
$R$ integral domain where every prime ideal is principal then set of non-principal ideals has maximal element
90314
Maximal ideals in $R[x]$
6507
Every prime ideal of height 1 in a UFD is principal
5360
Ideal contained in a finite union of prime ideals
109199
Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$