query: Let $A$ be a ring. If $\operatorname{Spec} A$ is a finite set, then $A$ is a noetherian ring?
positive_passages.docid: 26805
positive_passages.text: Non-Noetherian 0-dimensional ring
negative_passages.docid: 69141
negative_passages.text: Is every Noetherian module finitely generated?
negative_passages.docid: 112560
negative_passages.text: Simple Noetherian domain which is not a division ring
negative_passages.docid: 62227
negative_passages.text: Is a product of two Noetherian schemes over Spec $\mathbb Z$ a Noetherian scheme?
negative_passages.docid: 39755
negative_passages.text: In a faithfully flat ring extension, is $\operatorname{ht}I=\operatorname{ht}IS$ right?
negative_passages.docid: 14343
negative_passages.text: Every nonzero element in a finite ring is either a unit or a zero divisor
negative_passages.docid: 68167
negative_passages.text: Intersection of powers of an ideal in a Noetherian ring
negative_passages.docid: 29474
negative_passages.text: Compactness of $\operatorname{Spec}(A)$
negative_passages.docid: 85633
negative_passages.text: Rings of polynomials whose (partial) derivatives vanish are Noetherian?
negative_passages.docid: 92822
negative_passages.text: Finite number of elements generating the unit ideal of a commutative ring
negative_passages.docid: 65536
negative_passages.text: Finitely generated ideals in a Boolean ring are principal, why?
negative_passages.docid: 67470
negative_passages.text: If $S$ is a ring with the property that $s=s^2$ for each $s \in S$, then is $S$ commutative?
negative_passages.docid: 76047
negative_passages.text: Annihilators of elements of a finitely generated faithful module over a noetherian reduced ring
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: 116883
negative_passages.text: About ideals in a ring which is a $k$ vector space
negative_passages.docid: 141900
negative_passages.text: Exact sequence and Noetherian modules
negative_passages.docid: 54916
negative_passages.text: Maximal ideal in commutative ring