----
> [!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
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####
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#### 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
> ```