There exists a prime ideal not containing non-nilpotent element
67944
Nilpotent Elements and Intersection of Prime Ideals
90889
Prime ideals in a finite direct product of rings
86816
Example of two prime ideals whose intersection of the squares not equal to the square of the intersection
67669
Prime ideals of a finite direct product ring
139794
In a (not necessarily commutative) ring, a nilpotent maximal ideal is unique.
111114
Prove that an ideal in $k[x,y]$ is a prime ideal
36147
A finite group is nilpotent iff two elements with relatively prime order commute
6307
maximal ideal not containing some expression
56800
Intersection of prime ideals
139334
Determining the existence or non-existence of Non Trivial Ideals of $L(V)$
50809
Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set
127030
Simple example of non-arithmetic ring (non-distributive ideal lattice)
104486
Ideal in $\mathbb Z[x]$ which is not two-generated
154239
Can a prime in a Dedekind domain be contained in the union of the other prime ideals?
47134
Ideals generated by two elements
22544
Let R be a commutative ring, and let P be a prime ideal of R. Suppose that P has no nontrivial zero divisors in it. Show that R is an integral domain.
94157
Normal Ring and Prime Ideal whose Square is Principal