If $P$ is a prime ideal of $R$ and $X\subseteq P$ then there's a minimal ideal
105313
Existence of minimal prime ideal contained in given prime ideal and containing a given subset
93658
Proving that an ideal in a PID is maximal if and only if it is generated by an irreducible
93929
The height of a principal prime ideal
83009
Showing that $R(x)$ is a proper subset of $R((x))$ if $R$ is a field
81743
Prime ideals in $C[0,1]$
109199
Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$
111996
Maximal and Prime Ideal in Z
79897
if R is a commutative ring in which all the prime ideals are finitely generated then R is Noetherian
3327
Height and minimal number of generators of an ideal
45962
Show that any prime ideal from such a ring is maximal.
19230
Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
7833
Ideal and minimal polynomial
67669
Prime ideals of a finite direct product ring
96071
How to show that a prime ideal of height 2 can’t necessarily be generated by 2 elements? (Hartshorne exercise I.1.11)
34807
Localization at finitely many minimal prime ideals
92585
If krull dimension is $0$, then all prime ideals are maximal?
144250
subideals of an ideal