Prime ideal in $R[x]$ lying above $P$
133975
Localising a polynomial ring and non-maximal prime ideal
13901
Finitely many prime ideals lying over $\mathfrak{p}$
45962
Show that any prime ideal from such a ring is maximal.
114193
On the absolute norm of an ideal
108380
Assume $P$ is a prime ideal s.t. $K \subset P$, show $f(P)$ is a prime ideal
42170
$R$ integral domain where every prime ideal is principal then set of non-principal ideals has maximal element
116453
Is any quotient of a Euclidean domain by a prime ideal a Euclidean domain?
116000
Prove that prime ideals of a finite ring are maximal
148788
Polynomial ring ideal. Show that $(f) \cap R_N = (0) \iff f \notin R_N$
6699
An ideal that is maximal among non-finitely generated ideals is prime.
75558
Counter-example for prime ideals in a non commutative ring.
138114
Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
131497
Maximal ideal not containing the set of powers of an element is prime
22544
Let R be a commutative ring, and let P be a prime ideal of R. Suppose that P has no nontrivial zero divisors in it. Show that R is an integral domain.
29126
Maximal ideal in the ring of continuous functions from $\mathbb{R} \to \mathbb{R}$
50809
Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set
90314
Maximal ideals in $R[x]$