query: Any module is projective iff any module is injective
positive_passages.docid: 148111
positive_passages.text: Every $R$-module is projective if and only if every $R$-module is injective
negative_passages.docid: 137029
negative_passages.text: Prove that $\operatorname{Hom}_{\Bbb{Z}}(\Bbb{Q},\Bbb{Z}) = 0$ and show that $\Bbb{Q}$ is not a projective $\Bbb{Z}$-module.
negative_passages.docid: 69141
negative_passages.text: Is every Noetherian module finitely generated?
negative_passages.docid: 126472
negative_passages.text: Surjective endomorphisms of uniserial modules
negative_passages.docid: 111239
negative_passages.text: Are monomorphisms of rings injective?
negative_passages.docid: 37479
negative_passages.text: Proper submodules of Noetherian modules are intersections of indecomposable modules
negative_passages.docid: 109610
negative_passages.text: Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
negative_passages.docid: 149275
negative_passages.text: Origin of the terminology projective module
negative_passages.docid: 51245
negative_passages.text: $A \longrightarrow \text{Im} f$ is an epimorphism and a cokernel of ker $f \longrightarrow A$ in every abelian category
negative_passages.docid: 37058
negative_passages.text: Induced maps in homology are injective
negative_passages.docid: 84301
negative_passages.text: Showing that some Function on the Unit Disc is injective
negative_passages.docid: 47630
negative_passages.text: Endomorphisms of modules satisfying chain conditions and counterexamples.
negative_passages.docid: 70912
negative_passages.text: If $g\circ f$ is injective and $f$ is surjective then $g$ is injective
negative_passages.docid: 111140
negative_passages.text: Constant morphism between projective varieties
negative_passages.docid: 11202
negative_passages.text: If $g \circ f$ is injective, so is $g$
negative_passages.docid: 140938
negative_passages.text: Finitely generated projective module
negative_passages.docid: 17978
negative_passages.text: Isomorphism classes of $\mathbb{Z}[i]$ modules.