In a finite ring extension there are only finitely many prime ideals lying over a given prime ideal
13901
Finitely many prime ideals lying over $\mathfrak{p}$
50809
Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set
5360
Ideal contained in a finite union of prime ideals
140553
An ideal which is not finitely generated
67669
Prime ideals of a finite direct product ring
105313
Existence of minimal prime ideal contained in given prime ideal and containing a given subset
94532
How to prove a commutative, with unit, Noetherian ring $A$ only has finitely many minimal prime ideals via the following step?
21604
A complete ring with respect to an ideal
138114
Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
74681
A finite extension with finitely many intermediate fields is simple
107002
Noetherian ring whose ideals have arbitrarily large number of generators
138882
A prime poset of ideals
51578
Noetherian ring with finitely many height $n$ primes
67342
Why does a minimal prime ideal consist of zerodivisors?
53770
Let $R$ be a finite commutative ring. Show that an ideal is maximal if and only if it is prime.
74796
Extension of intersection of ideals
81221
The prime number theorem over a finite field - Lang's *Algebra*, Chapter V, Exercise 23(b)