query: Noetherian ring is finitely generated
positive_passages.docid: 144623
positive_passages.text: Can one avoid AC in the proof that in Noetherian rings there is a maximal element for each set?
negative_passages.docid: 127044
negative_passages.text: Prove that a finitely-generated free module has a finite basis
negative_passages.docid: 117211
negative_passages.text: Infinite linear independent family in a finitely generated $A$-module
negative_passages.docid: 26805
negative_passages.text: Non-Noetherian 0-dimensional ring
negative_passages.docid: 16727
negative_passages.text: Intersection of finitely generated ideals
negative_passages.docid: 51593
negative_passages.text: Every finite commutative ring with no zero divisors contains a multiplicative identity?
negative_passages.docid: 9806
negative_passages.text: $M$ finitely generated if submodule and quotient are finitely generated.
negative_passages.docid: 59687
negative_passages.text: Suppose $M$ is a finitely generated module over $R$ where $R$ is a Noetherian ring. Prove that $M$ is a noetherian module.
negative_passages.docid: 99423
negative_passages.text: Is it true every ideal of $\mathbb{Z}[x]$ is finitely generated?
negative_passages.docid: 62917
negative_passages.text: Associated Prime Ideals in a Noetherian Ring; Exercise 6.4 in Matsumura
negative_passages.docid: 116955
negative_passages.text: Showing the existence of a certain kind of extension of a finitely generated algebra
negative_passages.docid: 68926
negative_passages.text: Finitely generated singular homology
negative_passages.docid: 26368
negative_passages.text: Finitely generated graded modules over $K[x]$
negative_passages.docid: 74314
negative_passages.text: Noetherian ring and the same prime divisors
negative_passages.docid: 85633
negative_passages.text: Rings of polynomials whose (partial) derivatives vanish are Noetherian?
negative_passages.docid: 14055
negative_passages.text: How to show that a finite commutative ring without zero divisors is a field?
negative_passages.docid: 49303
negative_passages.text: In a noetherian integral domain every non invertible element is a product of irreducible elements