A prime ideal $\mathfrak{p} \subset \mathcal{O}_K$ lies above/over $p$ if $\mathfrak{p}\cap \mathbb{Z} = p\mathbb{Z}$
45098
How do we prove the "lying over" property for integral extensions?
107463
Is an ideal which is maximal with respect to the property that it consists of zero divisors necessarily prime?
87103
Quick question about ideals of field $F$ in $F[x]$ are principal.
110984
Ideals and prime ideals in a commutative ring.
74370
$P$ is a prime ideal of $R$ iff $R/P$ is an integral domain. : $P≠R$
58640
$R$ is an algebra over an infinite field. If $\exists$ ideals s.t. $J\subseteq \bigcup_{k=1}^nI_k$ then $J\subseteq I_k$ for some $k$
138114
Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
50809
Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set
91180
Show $R \setminus S$ is a union of prime ideals
53469
C(0, 1) has infinitely many prime ideals not of the form Mp
112045
A property of minimal prime ideal
74558
Localization of ideals at all primes
117536
Why is the localization at a prime ideal a local ring?
252
Why doesn't $0$ being a prime ideal in $\mathbb Z$ imply that $0$ is a prime number?
78455
Prove that a nonzero integer p is prime if and only if the ideal (p) is maximal in Z.
44083
prove that maximal ideal in $\mathbb{Z}$ generated by a prime number
126127
A field extension of prime degree