Proof Verification: Prove a nonzero, proper, prime ideal in a PID is maximal
53367
In a principal ideal domain, prove that every non trivial prime ideal is a maximal ideal. What could be wrong in this approach?
45962
Show that any prime ideal from such a ring is maximal.
105313
Existence of minimal prime ideal contained in given prime ideal and containing a given subset
119056
If in a UFD every maximal ideal is principal then it is a PID
18406
An ideal whose radical is maximal is primary
151829
Why are maximal ideals prime?
23099
Verifying that the ideal $(x^3-y^2)$ is prime
63659
If D is an Integral Domain and has finite characteristic p, prove p is prime.
112045
A property of minimal prime ideal
13901
Finitely many prime ideals lying over $\mathfrak{p}$
53770
Let $R$ be a finite commutative ring. Show that an ideal is maximal if and only if it is prime.
464
Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
104377
Maximal Ideals in Ring of Continuous Functions
146304
prove $(n)$ prime ideal of $\mathbb{Z}$ iff $n$ is prime or zero
130466
Proving every prime ideal is maximal in a finite dimensional ring over a field.
129371
Maximal ideals in the ring of real functions on $[0,1]$
34807
Localization at finitely many minimal prime ideals