query: Every projective module is a direct summand of free module.
positive_passages.docid: 21466
positive_passages.text: $P$ is projective . Show that $P$ is a direct summand of a free $R-$ module
negative_passages.docid: 60674
negative_passages.text: Finitely generated idempotent ideals are principal: proof without using Nakayama's lemma
negative_passages.docid: 153852
negative_passages.text: Example of modules that are projective but not free; torsion-free but not free
negative_passages.docid: 49948
negative_passages.text: If every ideal is principal show the same is true for the image of a homomorphism.
negative_passages.docid: 29019
negative_passages.text: Ideals in direct product of rings
negative_passages.docid: 33283
negative_passages.text: Every Artinian ring is isomorphic to a direct product of Artinian local rings
negative_passages.docid: 69398
negative_passages.text: Rank-nullity theorem for free $\mathbb Z$-modules
negative_passages.docid: 95942
negative_passages.text: $k[x]/(x^n)$ module with finite free resolution is free
negative_passages.docid: 141477
negative_passages.text: Decomposition of finitely generated graded modules over 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: 40996
negative_passages.text: Proving that free modules are flat (without appealing projective modules)
negative_passages.docid: 75625
negative_passages.text: Complete residue system proof
negative_passages.docid: 47630
negative_passages.text: Endomorphisms of modules satisfying chain conditions and counterexamples.
negative_passages.docid: 119999
negative_passages.text: A property of every real polynomial.
negative_passages.docid: 158062
negative_passages.text: Sum of free submodules of a module over a PID
negative_passages.docid: 148828
negative_passages.text: Submodule of a free module
negative_passages.docid: 5741
negative_passages.text: Direct product of abelian groups