query: Every free module is projective
positive_passages.docid: 141802
positive_passages.text: Prove that free modules are projective
negative_passages.docid: 41294
negative_passages.text: Permutation module of $S_n$
negative_passages.docid: 111307
negative_passages.text: If ideal $I$ of domain $R$ is free $R$-module, then $I$ is principal ideal.
negative_passages.docid: 144122
negative_passages.text: A problem about an $R$-module that is both injective and projective.
negative_passages.docid: 148111
negative_passages.text: Every $R$-module is projective if and only if every $R$-module is injective
negative_passages.docid: 142101
negative_passages.text: A direct product of projective modules which is not projective
negative_passages.docid: 123130
negative_passages.text: Showing an isomorphism between exterior products of a free module
negative_passages.docid: 122387
negative_passages.text: Is a stably free module always free?
negative_passages.docid: 102879
negative_passages.text: $\operatorname{Ext}$ and injectives, respectively projectives
negative_passages.docid: 65333
negative_passages.text: Weighted projective space and projective space are isomorphic
negative_passages.docid: 21466
negative_passages.text: $P$ is projective . Show that $P$ is a direct summand of a free $R-$ module
negative_passages.docid: 40996
negative_passages.text: Proving that free modules are flat (without appealing projective modules)
negative_passages.docid: 2719
negative_passages.text: Why isn't an infinite direct product of copies of $\Bbb Z$ a free module?
negative_passages.docid: 45576
negative_passages.text: A surjective homomorphism between finite free modules of the same rank
negative_passages.docid: 111140
negative_passages.text: Constant morphism between projective varieties
negative_passages.docid: 140340
negative_passages.text: Left and right R-modules
negative_passages.docid: 124864
negative_passages.text: A not free $\mathbb{Z}$-module