Example of a principal prime ideal containing a proper prime non-zero ideal.
93929
The height of a principal prime ideal
15904
Prime ideal and nilpotent elements
96071
How to show that a prime ideal of height 2 can’t necessarily be generated by 2 elements? (Hartshorne exercise I.1.11)
67203
Complement of maximal multiplicative set is a prime ideal
154239
Can a prime in a Dedekind domain be contained in the union of the other prime ideals?
112045
A property of minimal prime ideal
116453
Is any quotient of a Euclidean domain by a prime ideal a Euclidean domain?
127030
Simple example of non-arithmetic ring (non-distributive ideal lattice)
110022
Showing prime and maximal ideal
91180
Show $R \setminus S$ is a union of prime ideals
133975
Localising a polynomial ring and non-maximal prime ideal
33576
Non-principal ideal in $K[x,y]$?
75899
Principal ideal domain with finitely many ideals
85915
Principal prime ideals are minimal among prime ideals in a UFD
131497
Maximal ideal not containing the set of powers of an element is prime
138114
Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
78455
Prove that a nonzero integer p is prime if and only if the ideal (p) is maximal in Z.