Minimal prime of a ring is contraction of some prime ideal of any extension of the ring.
112045
A property of minimal prime ideal
138882
A prime poset of ideals
103518
If $J$ is the ideal generated by all idempotents in a prime ideal, then $R/J$ has only trivial idempotents
74314
Noetherian ring and the same prime divisors
105313
Existence of minimal prime ideal contained in given prime ideal and containing a given subset
85206
Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.
135586
Prove that the preimage of a prime ideal is also prime.
108380
Assume $P$ is a prime ideal s.t. $K \subset P$, show $f(P)$ is a prime ideal
63736
Every radical ideal in a Noetherian ring is a finite intersection of primes
76813
The ring $ℤ/nℤ$ is a field if and only if $n$ is prime
19883
Prime ideals of the matrix ring
53367
In a principal ideal domain, prove that every non trivial prime ideal is a maximal ideal. What could be wrong in this approach?
151829
Why are maximal ideals prime?
149203
Symbolic power of a prime ideal is primary
87780
Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither?
68167
Intersection of powers of an ideal in a Noetherian ring
110022
Showing prime and maximal ideal