Let $K$ be an algebraic number field. Prove that $O_K$ contains infinitely many prime ideals.
111287
number of prime ideals in algebraic integers
155771
Product of degree of two field extensions of prime degree
138114
Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
1702
Proving that there are infinitely many primes with remainder of 2 when divided by 3
76813
The ring $ℤ/nℤ$ is a field if and only if $n$ is prime
135586
Prove that the preimage of a prime ideal is also prime.
87103
Quick question about ideals of field $F$ in $F[x]$ are principal.
111114
Prove that an ideal in $k[x,y]$ is a prime ideal
89271
If $F$ is a field, then $F[x]$ is a principal ideal domain proof question
50809
Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set
92677
Infinite algebraic extension of a finite field
89313
Maximal ideals of polynomial rings in infinitely many variables
134896
Enlightening proof that the algebraic numbers form a field
7452
Splitting of primes in the compositum of fields
35821
Infinitely many primes for quadratic residues
106550
The bijection between homogeneous prime ideals of $S_f$ and prime ideals of $(S_f)_0$
131943
How to directly prove that $M$ is maximal ideal of $A$ iff $A/M$ is a field?