----- Let $R$ and $S$ be [[ring|rings]]. > [!proposition] Proposition. ([[ring homomorphism is injective iff kernel is trivial iff is a monomorphism]]) > A [[ring homomorphism]] $\varphi:R \to S$ is an [[injection]] if and only its [[kernel of a ring homomorphism|kernel]] is trivial, if and only if it is a [[monomorphism]]. ^proposition ----- #### ---- #### 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 > ```