query: Structure theorem of modules in the graded case
positive_passages.docid: 26368
positive_passages.text: Finitely generated graded modules over $K[x]$
negative_passages.docid: 23037
negative_passages.text: Computing the order of $\mathrm{SL}_2(\mathbb F_p)$ as the kernel of $\mathrm{GL}_2(\mathbb F_p)$
negative_passages.docid: 103349
negative_passages.text: A question about a proof of Noetherian modules and exact sequences
negative_passages.docid: 44983
negative_passages.text: Isomorphism of R-modules
negative_passages.docid: 141149
negative_passages.text: Proof some module is direct sum by its submodules.
negative_passages.docid: 99707
negative_passages.text: free module implies surjective map of affine schemes
negative_passages.docid: 17304
negative_passages.text: Tensor product of two finitely-generated modules over a local ring is zero
negative_passages.docid: 37479
negative_passages.text: Proper submodules of Noetherian modules are intersections of indecomposable modules
negative_passages.docid: 36987
negative_passages.text: A criterion of flat modules
negative_passages.docid: 144122
negative_passages.text: A problem about an $R$-module that is both injective and projective.
negative_passages.docid: 104784
negative_passages.text: On the grade of an ideal
negative_passages.docid: 140938
negative_passages.text: Finitely generated projective module
negative_passages.docid: 99198
negative_passages.text: Principal ideal and free module
negative_passages.docid: 70872
negative_passages.text: Isomorphism of quotient modules implies isomorphism of submodules?
negative_passages.docid: 136804
negative_passages.text: Computing $\mathrm{Hom}(\mathbb Z_n,\mathbb Z_m)$ as $\mathbb Z$-module
negative_passages.docid: 69398
negative_passages.text: Rank-nullity theorem for free $\mathbb Z$-modules
negative_passages.docid: 63541
negative_passages.text: Projective and injective modules; direct sums and products