---- > [!definition] Definition. ([[commutative algebra]]) > The situation outlined in [[algebra]] simplifies if the [[ring|rings]] $R,S$ are *both* [[commutative ring|commutative]]. In this case the 'center condition' goes away, and we may just define a **commutative $R$-algebra** as a [[ring homomorphism]] $\alpha:R \to S$ and/or the $R$-[[module]] structure on $S$ it induces (cf. [[module induced by a ring homomorphism]]). ^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 > ```