---- > [!definition] Definition. ([[split epimorphism]]) >Let $R$ be a [[ring]]. An $R$-[[module]] [[linear map|homomorphism]] $\varphi:M \to N$ is called a **split monomorphism** if it admits a [[inverse map|left-inverse]]. ^definition > [!equivalence] > Here is where the name comes from: [[characterization of left and right inverses in R-mod]]. > ---- #### ---- #### 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 > ```