Show every prime ideal in $\mathbb{Z}$ is of form $\langle p\rangle$ where $p$ is prime.
111996
Maximal and Prime Ideal in Z
13901
Finitely many prime ideals lying over $\mathfrak{p}$
84386
Domain strictly contained in the intersection of localizations at the primes of height one
102282
Let $R$ be a PID, and let $\pi\in R$ be prime. Is it $R/\langle\pi\rangle \times R/\langle \pi\rangle$ a cyclic $R$-module?
110022
Showing prime and maximal ideal
91180
Show $R \setminus S$ is a union of prime ideals
144572
Proof that ideals in $C[0,1]$ are of the form $M_c$ that should not involve Zorn's Lemma
74370
$P$ is a prime ideal of $R$ iff $R/P$ is an integral domain. : $P≠R$
57669
A proof that $\mathbb{Z}_{p}$ is an integral domain if and only if $p$ is prime.
43230
Is $\langle1-i\rangle$ a maximal ideal in $\mathbb{Z}[i]$?
44083
prove that maximal ideal in $\mathbb{Z}$ generated by a prime number
149747
Prove that if I is a prime ideal of R then I[x] is a prime ideal of R[x]
19740
What's are all the prime elements in Gaussian integers $\mathbb{Z}[i]$
90144
Show that if $a+bi$ is irreducible over $\mathbb{Z} [i]$ then $a^2 + b^2$ is prime over $\mathbb{Z} $
155745
Ideals of $\mathbb{Z}[X]$
97740
Homogeneous ideals are contained in homogeneous prime ideals
91622
Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.