---- > [!definition] Definition. ([[algebraic element]]) > Let $A$ be an $R$-[[algebra]] (assume commutative). An element $x \in A$ is **$R$-algebraic** if there is a [[polynomial 4|polynomial]] $f \in R[T]$ such that $f(x)=0$. ^definition > [!specialization] > [[integral element of an algebra|Integral elements]] are those for which $f$ is in fact [[monic polynomial|monic]]. ^specialization ---- #### ---- #### 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 > ```