query: Property of free submodules for a module over a PID
positive_passages.docid: 158062
positive_passages.text: Sum of free submodules of a module over a PID
negative_passages.docid: 34065
negative_passages.text: Submodule of free module over a p.i.d. is free even when the module is not finitely generated?
negative_passages.docid: 28518
negative_passages.text: Hom of finitely generated modules over a noetherian ring
negative_passages.docid: 40996
negative_passages.text: Proving that free modules are flat (without appealing projective modules)
negative_passages.docid: 29231
negative_passages.text: Proof of : $x^{n}\equiv x^{\varphi(m)+[n \bmod \varphi(m)]} \mod m$
negative_passages.docid: 70872
negative_passages.text: Isomorphism of quotient modules implies isomorphism of submodules?
negative_passages.docid: 93658
negative_passages.text: Proving that an ideal in a PID is maximal if and only if it is generated by an irreducible
negative_passages.docid: 47630
negative_passages.text: Endomorphisms of modules satisfying chain conditions and counterexamples.
negative_passages.docid: 152721
negative_passages.text: Help showing $H_n=\sum_{h \in H}h \in F[H]$ is a simple submodule
negative_passages.docid: 34754
negative_passages.text: Why is the polynomial ring of more than one variable not a PID?
negative_passages.docid: 129399
negative_passages.text: Maximum module principle
negative_passages.docid: 147157
negative_passages.text: Modules over commutative rings
negative_passages.docid: 117208
negative_passages.text: Smith Normal Form for PIDs
negative_passages.docid: 4652
negative_passages.text: Is $V$ a simple $\text{End}_kV$-module?
negative_passages.docid: 35745
negative_passages.text: Question about a submodule
negative_passages.docid: 73825
negative_passages.text: Every $R$-module is a quotient of a free module
negative_passages.docid: 126503
negative_passages.text: Showing that an integral domain is a PID if it satisfies two conditions