query: Finitely generated module with a submodule that is not finitely generated
positive_passages.docid: 4624
positive_passages.text: Example of a finitely generated module with submodules that are not finitely generated
negative_passages.docid: 37479
negative_passages.text: Proper submodules of Noetherian modules are intersections of indecomposable modules
negative_passages.docid: 158062
negative_passages.text: Sum of free submodules of a module over a PID
negative_passages.docid: 18329
negative_passages.text: How do I remove a submodule?
negative_passages.docid: 69141
negative_passages.text: Is every Noetherian module finitely generated?
negative_passages.docid: 102072
negative_passages.text: Simple $M_n(D)$-module with $D$ a division ring
negative_passages.docid: 95930
negative_passages.text: Finitely generated modules over a Noetherian ring are Noetherian
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: 74974
negative_passages.text: When $\operatorname{Hom}_{R}(M,N)$ is finitely generated as $\mathbb Z$-module or $R$-module?
negative_passages.docid: 141477
negative_passages.text: Decomposition of finitely generated graded modules over PID
negative_passages.docid: 117211
negative_passages.text: Infinite linear independent family in a finitely generated $A$-module
negative_passages.docid: 86724
negative_passages.text: Example of a non-zero module that has no associated primes
negative_passages.docid: 140553
negative_passages.text: An ideal which is not finitely generated
negative_passages.docid: 101095
negative_passages.text: Constructing an example s.t. $\operatorname{Hom}_R(M,N)$ is not finitely generated
negative_passages.docid: 12474
negative_passages.text: Does an injective endomorphism of a finitely-generated free R-module have nonzero determinant?
negative_passages.docid: 142101
negative_passages.text: A direct product of projective modules which is not projective
negative_passages.docid: 141149
negative_passages.text: Proof some module is direct sum by its submodules.