Let S be the set of non ﬁnitely generated ideals in R. Suppose A is a maximal element in S. Then A is a prime ideal
6699
An ideal that is maximal among non-finitely generated ideals is prime.
109199
Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$
57198
How to show that a valuation ring has a unique maximal ideal?
5360
Ideal contained in a finite union of prime ideals
107463
Is an ideal which is maximal with respect to the property that it consists of zero divisors necessarily prime?
45684
Is quotient of a ring by a power of a maximal ideal local?
104377
Maximal Ideals in Ring of Continuous Functions
134991
Commutative non Noetherian rings in which all maximal ideals are finitely generated
151829
Why are maximal ideals prime?
111114
Prove that an ideal in $k[x,y]$ is a prime ideal
115920
Showing $R$ is a local ring if and only if all elements of $R$ that are not units form an ideal
144623
Can one avoid AC in the proof that in Noetherian rings there is a maximal element for each set?
140553
An ideal which is not finitely generated
157876
If every prime ideal is maximal, what can we say about the ring?
30714
A question on ring homomorphisms and maximal ideals.
75558
Counter-example for prime ideals in a non commutative ring.
87780
Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither?