Not finitely generated ideal but only contained in finitely generated ideals implies ideal is prime
6699
An ideal that is maximal among non-finitely generated ideals is prime.
19230
Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
94532
How to prove a commutative, with unit, Noetherian ring $A$ only has finitely many minimal prime ideals via the following step?
116453
Is any quotient of a Euclidean domain by a prime ideal a Euclidean domain?
42652
Must $k$-subalgebra of $k[x]$ be finitely generated?
96071
How to show that a prime ideal of height 2 can’t necessarily be generated by 2 elements? (Hartshorne exercise I.1.11)
138114
Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
92585
If krull dimension is $0$, then all prime ideals are maximal?
103518
If $J$ is the ideal generated by all idempotents in a prime ideal, then $R/J$ has only trivial idempotents
107463
Is an ideal which is maximal with respect to the property that it consists of zero divisors necessarily prime?
95240
Show that $({\mathbb{Q}},+)$ is not finitely generated using the Fundamental Theorem of Finitely Generated Abelian Groups.
90889
Prime ideals in a finite direct product of rings
79897
if R is a commutative ring in which all the prime ideals are finitely generated then R is Noetherian
138168
Prove: The pre-image of an ideal is an ideal.
53770
Let $R$ be a finite commutative ring. Show that an ideal is maximal if and only if it is prime.
2995
A finite dimensional algebra over a field has only finitely many prime ideals and all of them are maximal
15137
Does $IJ=IK\implies J=K$ always hold for integral domain and finitely generated nonzero ideal $I$?