query: If every prime ideal in a ring $R$ is finitely generated, then $R$ is Noetherian?
positive_passages.docid: 79897
positive_passages.text: if R is a commutative ring in which all the prime ideals are finitely generated then R is Noetherian
negative_passages.docid: 45962
negative_passages.text: Show that any prime ideal from such a ring is maximal.
negative_passages.docid: 63736
negative_passages.text: Every radical ideal in a Noetherian ring is a finite intersection of primes
negative_passages.docid: 121008
negative_passages.text: A non-noetherian ring with all localizations noetherian
negative_passages.docid: 46717
negative_passages.text: If $M$ is a Noetherian $R$-module, then $R/\text{Ann}(M)$ is a Noetherian ring
negative_passages.docid: 21604
negative_passages.text: A complete ring with respect to an ideal
negative_passages.docid: 76047
negative_passages.text: Annihilators of elements of a finitely generated faithful module over a noetherian reduced ring
negative_passages.docid: 84663
negative_passages.text: $A$ local Noetherian ring with principal maximal ideal implies PIR?
negative_passages.docid: 52602
negative_passages.text: $K[X^2,X^3]\subset K[X]$ is a Noetherian domain and all its prime ideals are maximal
negative_passages.docid: 95930
negative_passages.text: Finitely generated modules over a Noetherian ring are Noetherian
negative_passages.docid: 130466
negative_passages.text: Proving every prime ideal is maximal in a finite dimensional ring over a field.
negative_passages.docid: 94532
negative_passages.text: How to prove a commutative, with unit, Noetherian ring $A$ only has finitely many minimal prime ideals via the following step?
negative_passages.docid: 92585
negative_passages.text: If krull dimension is $0$, then all prime ideals are maximal?
negative_passages.docid: 65536
negative_passages.text: Finitely generated ideals in a Boolean ring are principal, why?
negative_passages.docid: 92071
negative_passages.text: A maximal ideal is always a prime ideal?
negative_passages.docid: 16643
negative_passages.text: A slick proof that a field which is finitely generated as a ring is finite
negative_passages.docid: 110984
negative_passages.text: Ideals and prime ideals in a commutative ring.