query: Are finitely generated submodules of finitely generated free modules free?
positive_passages.docid: 145758
positive_passages.text: Are submodules of finitely generated free modules always free?
negative_passages.docid: 93681
negative_passages.text: Integral closure of $\mathbb{Z}$ in $\mathbb{C}$ is not finitely generated as a $\mathbb{Z}$-module?
negative_passages.docid: 26368
negative_passages.text: Finitely generated graded modules over $K[x]$
negative_passages.docid: 153622
negative_passages.text: Are intermediate rings of finitely generated ring extensions also finitely generated?
negative_passages.docid: 141802
negative_passages.text: Prove that free modules are projective
negative_passages.docid: 76047
negative_passages.text: Annihilators of elements of a finitely generated faithful module over a noetherian reduced ring
negative_passages.docid: 39652
negative_passages.text: Quotient of free module
negative_passages.docid: 70872
negative_passages.text: Isomorphism of quotient modules implies isomorphism of submodules?
negative_passages.docid: 120637
negative_passages.text: Is there a unique cyclic submodule for every factor dividing the order of a cyclic module?
negative_passages.docid: 4624
negative_passages.text: Example of a finitely generated module with submodules that are not finitely generated
negative_passages.docid: 128489
negative_passages.text: Linearly independent elements are less than generators in a module.
negative_passages.docid: 92822
negative_passages.text: Finite number of elements generating the unit ideal of a commutative ring
negative_passages.docid: 157236
negative_passages.text: Tensor product of modules.
negative_passages.docid: 69141
negative_passages.text: Is every Noetherian module finitely generated?
negative_passages.docid: 114640
negative_passages.text: Showing that an ideal is not a free $R-$module.
negative_passages.docid: 28518
negative_passages.text: Hom of finitely generated modules over a noetherian ring
negative_passages.docid: 8417
negative_passages.text: Natural $(R/I)$-module structure for an $R$-module $M$ annihilated by $I$