---- > [!definition] Definition. ([[characterization of projective modules]]) > Let $R$ be a [[commutative ring|(say, commutative)]] [[ring]]. An $R$-[[module]] $Q$ is **injective** if the [[hom functor|hom]] [[contravariant functor|functor]] $\text{Hom}_{R\text{-}\mathsf{Mod}}(-, Q)$ is [[exact functor|exact]]. ^definition ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```