Does every prime ideal of a ring contain a minimal prime?
105313
Existence of minimal prime ideal contained in given prime ideal and containing a given subset
63736
Every radical ideal in a Noetherian ring is a finite intersection of primes
53367
In a principal ideal domain, prove that every non trivial prime ideal is a maximal ideal. What could be wrong in this approach?
27916
Are the determinantal ideals prime?
84663
$A$ local Noetherian ring with principal maximal ideal implies PIR?
29019
Ideals in direct product of rings
147871
How do the prime ideals of $\mathbb{Z}_{k}$ look like?
7833
Ideal and minimal polynomial
133975
Localising a polynomial ring and non-maximal prime ideal
6646
A (non-artificial) example of a ring without maximal ideals
155991
Is it the case that every quotient ring ${F[x]}/{(p(x))}$ is a PID?
34807
Localization at finitely many minimal prime ideals
54916
Maximal ideal in commutative ring
5360
Ideal contained in a finite union of prime ideals
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.
85206
Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.
109199
Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$