query: Natural structure of (R/I)-Module
positive_passages.docid: 8417
positive_passages.text: Natural $(R/I)$-module structure for an $R$-module $M$ annihilated by $I$
negative_passages.docid: 50212
negative_passages.text: $R/Ra$ is an injective module over itself
negative_passages.docid: 74445
negative_passages.text: Noetherian and Artinian modules
negative_passages.docid: 44983
negative_passages.text: Isomorphism of R-modules
negative_passages.docid: 117211
negative_passages.text: Infinite linear independent family in a finitely generated $A$-module
negative_passages.docid: 109649
negative_passages.text: idempotents acting as local identities
negative_passages.docid: 58028
negative_passages.text: Semisimplicity is equivalent to each simple left module is projective?
negative_passages.docid: 73662
negative_passages.text: Example of non-flat modules
negative_passages.docid: 26244
negative_passages.text: Pathologies in module theory
negative_passages.docid: 158583
negative_passages.text: Prove that if $M$ is an $R-$ projective left module then $M/IM$ is an $R/I-$ projective left module.
negative_passages.docid: 145758
negative_passages.text: Are submodules of finitely generated free modules always free?
negative_passages.docid: 73825
negative_passages.text: Every $R$-module is a quotient of a free module
negative_passages.docid: 148828
negative_passages.text: Submodule of a free module
negative_passages.docid: 4624
negative_passages.text: Example of a finitely generated module with submodules that are not finitely generated
negative_passages.docid: 139828
negative_passages.text: Finitely Presented Modules and Exact Sequences
negative_passages.docid: 40705
negative_passages.text: If $M$ is an $R$-module and $I\subseteq\mathrm{Ann}(M)$ an ideal, then $M$ has a structure of $R/I$-module
negative_passages.docid: 128489
negative_passages.text: Linearly independent elements are less than generators in a module.