A Commutative Ring Having a Unique Prime Ideal (Dummit and Foote, Prob 7.4.40(i))
103830
Each element of a ring is either a unit or a nilpotent element iff the ring has a unique prime ideal
139794
In a (not necessarily commutative) ring, a nilpotent maximal ideal is unique.
62917
Associated Prime Ideals in a Noetherian Ring; Exercise 6.4 in Matsumura
57198
How to show that a valuation ring has a unique maximal ideal?
111996
Maximal and Prime Ideal in Z
117536
Why is the localization at a prime ideal a local ring?
82609
Ring such that $x^4=x$ for all $x$ is commutative
110022
Showing prime and maximal ideal
111114
Prove that an ideal in $k[x,y]$ is a prime ideal
52966
Rings, ideals and units-proof
11573
Rings and some of their properties
137450
Two-sided ideal generated by subset of not commutative ring
135682
Are distinct prime ideals in a ring always coprime? If not, then when are they?
69649
If an ideal contains the multiplicative identity, then it is the whole ring
107002
Noetherian ring whose ideals have arbitrarily large number of generators
74314
Noetherian ring and the same prime divisors
105313
Existence of minimal prime ideal contained in given prime ideal and containing a given subset