Does a prime ideal map to a prime ideal?
108380
Assume $P$ is a prime ideal s.t. $K \subset P$, show $f(P)$ is a prime ideal
6699
An ideal that is maximal among non-finitely generated ideals is prime.
135682
Are distinct prime ideals in a ring always coprime? If not, then when are they?
83050
Show that $P[x]+\langle x\rangle $ is a prime ideal of $R[x]$.
53469
C(0, 1) has infinitely many prime ideals not of the form Mp
19883
Prime ideals of the matrix ring
85915
Principal prime ideals are minimal among prime ideals in a UFD
90889
Prime ideals in a finite direct product of rings
67342
Why does a minimal prime ideal consist of zerodivisors?
154239
Can a prime in a Dedekind domain be contained in the union of the other prime ideals?
147871
How do the prime ideals of $\mathbb{Z}_{k}$ look like?
78455
Prove that a nonzero integer p is prime if and only if the ideal (p) is maximal in Z.
149747
Prove that if I is a prime ideal of R then I[x] is a prime ideal of R[x]
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.
157876
If every prime ideal is maximal, what can we say about the ring?
112045
A property of minimal prime ideal
107463
Is an ideal which is maximal with respect to the property that it consists of zero divisors necessarily prime?