Any prime ideal of $R[x]$ properly containing $M[x]$ is a maximal ideal of $R[x]$
90314
Maximal ideals in $R[x]$
19230
Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
50809
Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set
76661
Checking the maximality of a principal ideal in $R[x]$
116000
Prove that prime ideals of a finite ring are maximal
136654
$(x_1-a_1, x_2-a_2)$ is a maximal ideal of $K[x_1,x_2]$
92585
If krull dimension is $0$, then all prime ideals are maximal?
109199
Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$
81743
Prime ideals in $C[0,1]$
46040
Preimage of maximal ideal is maximal (why is this answer wrong?)
53367
In a principal ideal domain, prove that every non trivial prime ideal is a maximal ideal. What could be wrong in this approach?
151829
Why are maximal ideals prime?
13901
Finitely many prime ideals lying over $\mathfrak{p}$
18406
An ideal whose radical is maximal is primary
40705
If $M$ is an $R$-module and $I\subseteq\mathrm{Ann}(M)$ an ideal, then $M$ has a structure of $R/I$-module
113582
How can I find an element $x\not\in\mathfrak mM_{\mathfrak m}$ for every maximal ideal $\mathfrak m$
67203
Complement of maximal multiplicative set is a prime ideal