---- Let $R$ be a [[ring]] and $A$ be an $R$-[[algebra]]. > [!definition] Definition. ([[subalgebra]]) > An $R$-**subalgebra** of $A$ is a [[subring]] $B \subset A$ to which the structure [[ring homomorphism]] $R \to A$ restricts. That is, $B$ is a [[subring]] of $A$ lying in the image of $R$: $r\cdot1_{A} \in B$ for all $r \in R$. ^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 > ```